origin of mass lect. 3: approach · origin of mass lect. 3: approach alfredo raya contents dcsb and...
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![Page 1: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/1.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Origin of MassLect. 3: Approach
Alfredo Raya
IFM-UMSNH
XIII Mexican School of Particles and Fields, San Carlos,Sonora, Mexico.
![Page 2: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/2.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Contents
Dynamical Chiral Symmetry Breaking and Confinement inQCD
A Toy Model: QED3
Confinement in QED3
Final Remarks
![Page 3: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/3.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Contents
Dynamical Chiral Symmetry Breaking and Confinement inQCD
A Toy Model: QED3
Confinement in QED3
Final Remarks
![Page 4: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/4.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Contents
Dynamical Chiral Symmetry Breaking and Confinement inQCD
A Toy Model: QED3
Confinement in QED3
Final Remarks
![Page 5: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/5.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Contents
Dynamical Chiral Symmetry Breaking and Confinement inQCD
A Toy Model: QED3
Confinement in QED3
Final Remarks
![Page 6: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/6.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
S−1F (p) = Z2 S
(0) −1F (p)
+g2 Z1F CF
∫d4k
16π4γµ SF (k) Γν(k, p)∆µν(k − p)
The solution is of the form
SF (p) =F (p2)
6p −M(p2)
![Page 7: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/7.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
S−1F (p) = Z2 S
(0) −1F (p)
+g2 Z1F CF
∫d4k
16π4γµ SF (k) Γν(k, p)∆µν(k − p)
The solution is of the form
SF (p) =F (p2)
6p −M(p2)
![Page 8: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/8.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
S−1F (p) = Z2 S
(0) −1F (p)
+g2 Z1F CF
∫d4k
16π4γµ SF (k) Γν(k, p)∆µν(k − p)
The solution is of the form
SF (p) =F (p2)
6p −M(p2)
![Page 9: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/9.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
Adapted from nucl-th/0007054.
![Page 10: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/10.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
g2
∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)
should have an enormous support.
I Strength of interaction g → geff (p)
![Page 11: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/11.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
g2
∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)
should have an enormous support.
I Strength of interaction g → geff (p)
![Page 12: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/12.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
g2
∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)
should have an enormous support.
I The Quark-Gluon Vertex
Adapted from Nucl. Phys. Proc. Suppl. 152 43, (2006).
![Page 13: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/13.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
g2
∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)
should have an enormous support.
I The Ghost and Gluon Propagators
Adapted from Braz. J. Phys. 37 201 (2007).
![Page 14: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/14.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Dynamical Mass Generation in QCD
g2
∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)
should have an enormous support.
I The Gluon Propagator is IR finite!
Adapted from PoS LAT2007, 297 (2007).
![Page 15: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/15.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Confinement can be studied through the IR properties ofGreen’s functions
![Page 16: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/16.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
I Ghost-Gluon vertex is IR finite
I Ghost propagator is IR divergent
I Gluon propagator is IR suppressed
![Page 17: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/17.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
I Ghost-Gluon vertex is IR finite
I Ghost propagator is IR divergent
I Gluon propagator is IR suppressed
![Page 18: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/18.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
I Ghost-Gluon vertex is IR finite
I Ghost propagator is IR divergent
I Gluon propagator is IR suppressed
![Page 19: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/19.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
Adapted from Nucl. Phys. Proc. Suppl. 152 43, (2006).
![Page 20: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/20.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
Adapted from Braz. J. Phys. 37 201 (2007).
![Page 21: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/21.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Kugo-Ojima criterion:
Adapted from PoS LAT2007, 297 (2007).
![Page 22: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/22.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Axiom of Reflexion Positivity
∆(t) =
∫d3x
∫d4p
(2π)4e i(tp4+~x ·~p)σ(p2)
=1
π
∫ ∞0
dp4 cos(tp4)σ(p24) ≥ 0 ,
with
σ(p2) =F (p2)M(p2)
p2 + M2(p2).
![Page 23: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/23.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QCD
Adapted from J. Phys. G32, R253 (2006).
![Page 24: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/24.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
A Toy Model
![Page 25: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/25.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 26: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/26.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 27: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/27.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 28: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/28.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 29: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/29.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 30: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/30.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 31: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/31.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 32: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/32.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 33: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/33.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Why QED3?
I Is super renormalizable
I Exhibits DCSB and Confinement
I Provides a popular battleground for lattice andcontinuum studies
I Exhibits special features of spin and statistics (anyons)and discrete symmetries
I The Chern-Simons term adds to its structural richness
I Has useful applications in Condensed Matter Physics
I High-Tc superconductivity
I Quantum Hall Effect
I Graphene
![Page 34: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/34.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
SDE in QED3
Corresponds to
S−1F (p) = S
(0) −1F (p)
+e2
∫d3k
(2π)3γµ SF (k) Γν(k , p)∆µν(k − p)
![Page 35: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/35.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
SDE in QED3
Corresponds to
S−1F (p) = S
(0) −1F (p)
+e2
∫d3k
(2π)3γµ SF (k) Γν(k , p)∆µν(k − p)
![Page 36: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/36.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Rainbow Truncation
I We start by neglecting fermion loops, G (q) = 1
I In Landau gauge, it corresponds to a photon propagator
∆(0)µν (q) =
1
q2
(gµν −
qµqνq2
)
I With a suitable choice of the electron-photon vertex,the electron propagator can be found self-consistently
![Page 37: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/37.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Rainbow Truncation
I We start by neglecting fermion loops, G (q) = 1
I In Landau gauge, it corresponds to a photon propagator
∆(0)µν (q) =
1
q2
(gµν −
qµqνq2
)
I With a suitable choice of the electron-photon vertex,the electron propagator can be found self-consistently
![Page 38: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/38.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Rainbow Truncation
I We start by neglecting fermion loops, G (q) = 1
I In Landau gauge, it corresponds to a photon propagator
∆(0)µν (q) =
1
q2
(gµν −
qµqνq2
)
I With a suitable choice of the electron-photon vertex,the electron propagator can be found self-consistently
![Page 39: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/39.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Rainbow Truncation
I Possible the simplest choice for the vertex isΓν(k , p) = γν
I This corresponds to the diagram
![Page 40: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/40.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Rainbow Truncation
I Possible the simplest choice for the vertex isΓν(k , p) = γν
I This corresponds to the diagram
![Page 41: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/41.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Solving the SDE
I In Rainbow Approximation
S−1F (p) = S
(0) −1F (p)
+4πα
∫d3k
(2π)3γµ SF (k) γν∆(0)
µν (k − p)
I Starting with massless fermions, m0 = 0, multiplying by
1 and 6p and taking trace and contracting with ∆(0)µν
1
F (p)= 1 +
α
2π2p2
∫d3k
F (k)
k2 + M2(k)
1
(k − p)4×[
− 2(k · p)2 + (2− ξ)(k2 + p2)k · p − 2(1− ξ)k2p2
]M(p)
F (p)=
α(2 + ξ)
2π2
∫d3k
F (k)M(k)
k2 + M2(k)
1
(k − p)2
![Page 42: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/42.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Solving the SDE
I In Rainbow Approximation
S−1F (p) = S
(0) −1F (p)
+4πα
∫d3k
(2π)3γµ SF (k) γν∆(0)
µν (k − p)
I Starting with massless fermions, m0 = 0, multiplying by
1 and 6p and taking trace and contracting with ∆(0)µν
1
F (p)= 1 +
α
2π2p2
∫d3k
F (k)
k2 + M2(k)
1
(k − p)4×[
− 2(k · p)2 + (2− ξ)(k2 + p2)k · p − 2(1− ξ)k2p2
]M(p)
F (p)=
α(2 + ξ)
2π2
∫d3k
F (k)M(k)
k2 + M2(k)
1
(k − p)2
![Page 43: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/43.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Solving the SDE
I Performing angular integrations
1
F (p)= 1− αξ
π2p
∫ ∞0
dkk2F (k)
k2 + M2(k)×[
1− k2 + p2
2kpln
∣∣∣∣k + p
k − p
∣∣∣∣]
M(p)
F (p)=
α(ξ + 2)
πp
∫ ∞0
dkkF (k)M(k)
k2 + M2(k)ln
∣∣∣∣k + p
k − p
∣∣∣∣
I In Landau gauge (ξ = 0)
M(p) =2α
πp
∫ ∞0
dkkM(k)
k2 + M2(k)ln
∣∣∣∣k + p
k − p
∣∣∣∣
![Page 44: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/44.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Solving the SDE
I Performing angular integrations
1
F (p)= 1− αξ
π2p
∫ ∞0
dkk2F (k)
k2 + M2(k)×[
1− k2 + p2
2kpln
∣∣∣∣k + p
k − p
∣∣∣∣]
M(p)
F (p)=
α(ξ + 2)
πp
∫ ∞0
dkkF (k)M(k)
k2 + M2(k)ln
∣∣∣∣k + p
k − p
∣∣∣∣I In Landau gauge (ξ = 0)
M(p) =2α
πp
∫ ∞0
dkkM(k)
k2 + M2(k)ln
∣∣∣∣k + p
k − p
∣∣∣∣
![Page 45: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/45.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
I We have an expression of the form
M(p) =
∫ ∞0
dk f (k,M(k); p,M(p))
≈∫ λ
κdk f (k ,M(k); p,M(p))
for κ→ 0 and λ→∞I Using some quadrature rule, we have
M(p) =Nmax∑j=1
wj f (kj ,M(kj ); p,M(p))
=Nmax∑j=1
wj f (kj ,Mj ; p,M(p))
where wj are the weights of the quadrature, kj thenodes and Mj = M(kj )
![Page 46: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/46.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
I We have an expression of the form
M(p) =
∫ ∞0
dk f (k,M(k); p,M(p))
≈∫ λ
κdk f (k ,M(k); p,M(p))
for κ→ 0 and λ→∞
I Using some quadrature rule, we have
M(p) =Nmax∑j=1
wj f (kj ,M(kj ); p,M(p))
=Nmax∑j=1
wj f (kj ,Mj ; p,M(p))
where wj are the weights of the quadrature, kj thenodes and Mj = M(kj )
![Page 47: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/47.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
I We have an expression of the form
M(p) =
∫ ∞0
dk f (k,M(k); p,M(p))
≈∫ λ
κdk f (k ,M(k); p,M(p))
for κ→ 0 and λ→∞I Using some quadrature rule, we have
M(p) =Nmax∑j=1
wj f (kj ,M(kj ); p,M(p))
=Nmax∑j=1
wj f (kj ,Mj ; p,M(p))
where wj are the weights of the quadrature, kj thenodes and Mj = M(kj )
![Page 48: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/48.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
I We have an expression of the form
M(p) =
∫ ∞0
dk f (k,M(k); p,M(p))
≈∫ λ
κdk f (k ,M(k); p,M(p))
for κ→ 0 and λ→∞I Using some quadrature rule, we have
M(p) =Nmax∑j=1
wj f (kj ,M(kj ); p,M(p))
=Nmax∑j=1
wj f (kj ,Mj ; p,M(p))
where wj are the weights of the quadrature, kj thenodes and Mj = M(kj )
![Page 49: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/49.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
![Page 50: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/50.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical TechniquesI Instead of solving the equation over an entire domain of
p, we decide that it is enough to know the massfunction only in a discrete set of points
I We can use the same points of the quadrature nodes
p → pj = kj
I We are then left with a system of nonlinear algebraicequations
M1 =Nmax∑j=1
wj f (kj ,Mj ; k1,M1)
M2 =Nmax∑j=1
wj f (kj ,Mj ; k2,M2)
Mk =Nmax∑j=1
wj f (kj ,Mj ; kk ,Mk)
![Page 51: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/51.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical TechniquesI Instead of solving the equation over an entire domain of
p, we decide that it is enough to know the massfunction only in a discrete set of points
I We can use the same points of the quadrature nodes
p → pj = kj
I We are then left with a system of nonlinear algebraicequations
M1 =Nmax∑j=1
wj f (kj ,Mj ; k1,M1)
M2 =Nmax∑j=1
wj f (kj ,Mj ; k2,M2)
Mk =Nmax∑j=1
wj f (kj ,Mj ; kk ,Mk)
![Page 52: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/52.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical TechniquesI Instead of solving the equation over an entire domain of
p, we decide that it is enough to know the massfunction only in a discrete set of points
I We can use the same points of the quadrature nodes
p → pj = kj
I We are then left with a system of nonlinear algebraicequations
M1 =Nmax∑j=1
wj f (kj ,Mj ; k1,M1)
M2 =Nmax∑j=1
wj f (kj ,Mj ; k2,M2)
Mk =Nmax∑j=1
wj f (kj ,Mj ; kk ,Mk)
![Page 53: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/53.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical TechniquesI Instead of solving the equation over an entire domain of
p, we decide that it is enough to know the massfunction only in a discrete set of points
I We can use the same points of the quadrature nodes
p → pj = kj
I We are then left with a system of nonlinear algebraicequations
M1 =Nmax∑j=1
wj f (kj ,Mj ; k1,M1)
M2 =Nmax∑j=1
wj f (kj ,Mj ; k2,M2)
Mk =Nmax∑j=1
wj f (kj ,Mj ; kk ,Mk)
![Page 54: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/54.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical TechniquesI Instead of solving the equation over an entire domain of
p, we decide that it is enough to know the massfunction only in a discrete set of points
I We can use the same points of the quadrature nodes
p → pj = kj
I We are then left with a system of nonlinear algebraicequations
M1 =Nmax∑j=1
wj f (kj ,Mj ; k1,M1)
M2 =Nmax∑j=1
wj f (kj ,Mj ; k2,M2)
Mk =Nmax∑j=1
wj f (kj ,Mj ; kk ,Mk )
![Page 55: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/55.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Numerical Techniques
![Page 56: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/56.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I To have an analytical insight, let us go back to
M(p) = 2α
∫d3k
2π2
M(k)
k2 + M2(k)
1
(k − p)2
I Linearize this expression substituting M2(k) = m2
M(p) =2α
2π2
∫d3k
M(k)
k2 + m2
1
(k − p)2
I Next, define
M(p) = (p2 + m2)χ(p), χ(r) =
∫d3k
(2π)3χ(k)e ikr
I It is straightforward to see that χ(r) verifies
d2
dr2χ(r) +
2
r
d
drχ(r) +
(m2 − 2α
r
)χ(r) = 0
![Page 57: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/57.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I To have an analytical insight, let us go back to
M(p) = 2α
∫d3k
2π2
M(k)
k2 + M2(k)
1
(k − p)2
I Linearize this expression substituting M2(k) = m2
M(p) =2α
2π2
∫d3k
M(k)
k2 + m2
1
(k − p)2
I Next, define
M(p) = (p2 + m2)χ(p), χ(r) =
∫d3k
(2π)3χ(k)e ikr
I It is straightforward to see that χ(r) verifies
d2
dr2χ(r) +
2
r
d
drχ(r) +
(m2 − 2α
r
)χ(r) = 0
![Page 58: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/58.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I To have an analytical insight, let us go back to
M(p) = 2α
∫d3k
2π2
M(k)
k2 + M2(k)
1
(k − p)2
I Linearize this expression substituting M2(k) = m2
M(p) =2α
2π2
∫d3k
M(k)
k2 + m2
1
(k − p)2
I Next, define
M(p) = (p2 + m2)χ(p), χ(r) =
∫d3k
(2π)3χ(k)e ikr
I It is straightforward to see that χ(r) verifies
d2
dr2χ(r) +
2
r
d
drχ(r) +
(m2 − 2α
r
)χ(r) = 0
![Page 59: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/59.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I To have an analytical insight, let us go back to
M(p) = 2α
∫d3k
2π2
M(k)
k2 + M2(k)
1
(k − p)2
I Linearize this expression substituting M2(k) = m2
M(p) =2α
2π2
∫d3k
M(k)
k2 + m2
1
(k − p)2
I Next, define
M(p) = (p2 + m2)χ(p), χ(r) =
∫d3k
(2π)3χ(k)e ikr
I It is straightforward to see that χ(r) verifies
d2
dr2χ(r) +
2
r
d
drχ(r) +
(m2 − 2α
r
)χ(r) = 0
![Page 60: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/60.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I A solution to this equation is
χ(r) = Ce−mr
I The constant C is fixed such that M(0) = m
I The Fourier transform of χ(r) yields
M(p) =m3
p2 + m2
I Expectedly, M(p → 0) ∼ m and M(p →∞) ∼ 1/p2.
![Page 61: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/61.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I A solution to this equation is
χ(r) = Ce−mr
I The constant C is fixed such that M(0) = m
I The Fourier transform of χ(r) yields
M(p) =m3
p2 + m2
I Expectedly, M(p → 0) ∼ m and M(p →∞) ∼ 1/p2.
![Page 62: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/62.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I A solution to this equation is
χ(r) = Ce−mr
I The constant C is fixed such that M(0) = m
I The Fourier transform of χ(r) yields
M(p) =m3
p2 + m2
I Expectedly, M(p → 0) ∼ m and M(p →∞) ∼ 1/p2.
![Page 63: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/63.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Analytical Insight
I A solution to this equation is
χ(r) = Ce−mr
I The constant C is fixed such that M(0) = m
I The Fourier transform of χ(r) yields
M(p) =m3
p2 + m2
I Expectedly, M(p → 0) ∼ m and M(p →∞) ∼ 1/p2.
![Page 64: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/64.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)
I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 65: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/65.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 66: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/66.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 67: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/67.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 68: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/68.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 69: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/69.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finite
I Confinement is reinstated
![Page 70: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/70.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
I The potential between two static charges in QED3 is
V (r) =e3G(0)
8πln(e2r) + cte +O
(1
r
)I Quenched approximation G(0) = 1
I There is confinement
I Including loops of massless fermions
G(q) =1
1 + e2Nf8q
→ 0 as q → 0
I Confinement is swept away
I Including loops of massive fermions, G(0) finiteI Confinement is reinstated
![Page 71: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/71.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Confinement in QED3
Adapted from nucl-th/0007054
![Page 72: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/72.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
Let us consider vacuum polarization effects into the SDE forthe fermion propagator
Consider Nf massless fermion families
This amounts to
G(q)
q2=
1
q2[1 + Π(q)]→ 1
q2 + e2Nf q8
![Page 73: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/73.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
Let us consider vacuum polarization effects into the SDE forthe fermion propagator
Consider Nf massless fermion families
This amounts to
G(q)
q2=
1
q2[1 + Π(q)]→ 1
q2 + e2Nf q8
![Page 74: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/74.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
Let us consider vacuum polarization effects into the SDE forthe fermion propagator
Consider Nf massless fermion families
This amounts to
G(q)
q2=
1
q2[1 + Π(q)]→ 1
q2 + e2Nf q8
![Page 75: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/75.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
The resulting equation in this case is, setting e2 = 1,
M(p) =1
2π2p
∫ ∞0
dkkM(k)
k2 + M2(k)ln
[k + p + Nf /8
|k − p|+ Nf /8
]
![Page 76: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/76.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
The resulting equation in this case is, setting e2 = 1,
M(p) =1
2π2p
∫ ∞0
dkkM(k)
k2 + M2(k)ln
[k + p + Nf /8
|k − p|+ Nf /8
]
![Page 77: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/77.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
The resulting equation in this case is, setting e2 = 1,
M(p) =1
2π2p
∫ ∞0
dkkM(k)
k2 + M2(k)ln
[k + p + Nf /8
|k − p|+ Nf /8
]
![Page 78: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/78.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I A more realistic situation would consider effectivescreening from fermion loops
I There will be a feed back between the amount of DGMand the screening
I Analyse the behavior of
e2
∫d3k γµ SF (k) Γν(k , p)∆µν(k − p)
![Page 79: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/79.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I A more realistic situation would consider effectivescreening from fermion loops
I There will be a feed back between the amount of DGMand the screening
I Analyse the behavior of
e2
∫d3k γµ SF (k) Γν(k , p)∆µν(k − p)
![Page 80: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/80.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I A more realistic situation would consider effectivescreening from fermion loops
I There will be a feed back between the amount of DGMand the screening
I Analyse the behavior of
e2
∫d3k γµ SF (k) Γν(k , p)∆µν(k − p)
![Page 81: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/81.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I Ward identity
I (k − p)νΓν = S−1F (k)− S−1
F (p)
I Restricts Π(q) to be gauge invatiant
I We end up with
M(p) ∼∫
dkF (k)M(k)
k2 + M2(k)
(F (k),F (p))
1 + Π(k − p)
![Page 82: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/82.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I Ward identity
I (k − p)νΓν = S−1F (k)− S−1
F (p)
I Restricts Π(q) to be gauge invatiant
I We end up with
M(p) ∼∫
dkF (k)M(k)
k2 + M2(k)
(F (k),F (p))
1 + Π(k − p)
![Page 83: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/83.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I Ward identity
I (k − p)νΓν = S−1F (k)− S−1
F (p)
I Restricts Π(q) to be gauge invatiant
I We end up with
M(p) ∼∫
dkF (k)M(k)
k2 + M2(k)
(F (k),F (p))
1 + Π(k − p)
![Page 84: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/84.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Vacuum Polarization Effects
I Ward identity
I (k − p)νΓν = S−1F (k)− S−1
F (p)
I Restricts Π(q) to be gauge invatiant
I We end up with
M(p) ∼∫
dkF (k)M(k)
k2 + M2(k)
(F (k),F (p))
1 + Π(k − p)
![Page 85: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/85.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restoration
I The vertex should be related to F (p) by the Wardidentity
I F (p) should be an homogeneous function of momentumin the IR :
F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 86: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/86.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restorationI The vertex should be related to F (p) by the Ward
identity
I F (p) should be an homogeneous function of momentumin the IR :
F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 87: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/87.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restorationI The vertex should be related to F (p) by the Ward
identityI F (p) should be an homogeneous function of momentum
in the IR :F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 88: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/88.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restorationI The vertex should be related to F (p) by the Ward
identityI F (p) should be an homogeneous function of momentum
in the IR :F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 89: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/89.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restorationI The vertex should be related to F (p) by the Ward
identityI F (p) should be an homogeneous function of momentum
in the IR :F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 90: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/90.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and ConfinementI Assume that the effective screening leads to chiral
symmetry restorationI The vertex should be related to F (p) by the Ward
identityI F (p) should be an homogeneous function of momentum
in the IR :F (ζp) = ζδF (p)
I Π(q) should also be homogeneous:
Π(ζq) = ζ−(1+δ)Π(q)
I Combining results
M(ζp) = M(p)!!
I There is an infrared collusion
![Page 91: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/91.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and Confinement
![Page 92: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/92.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
DMG and Confinement
![Page 93: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/93.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 94: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/94.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry Breaking
I Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 95: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/95.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 96: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/96.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equations
I Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 97: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/97.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomena
I Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 98: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/98.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 99: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/99.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulations
I Heavy Ion CollisionsI RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 100: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/100.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 101: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/101.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHIC
I LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 102: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/102.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 103: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/103.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter Systems
I SuperconductivityI Graphene
![Page 104: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/104.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI Superconductivity
I Graphene
![Page 105: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/105.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Elucidating the Origin of Mass has lead us to the studytwo very interesting phenomena
I Dynamical Chiral Symmetry BreakingI Confinement
I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions
I Compare against lattice simulationsI Heavy Ion Collisions
I RHICI LHC
I Condensed Matter SystemsI SuperconductivityI Graphene
![Page 106: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/106.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagators
I Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 107: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/107.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteria
I QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 108: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/108.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGV
I Simultaneity of Dynamical Symmetry Restoration andDeconfinement in HIC
I Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 109: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/109.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HIC
I Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 110: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/110.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic Fields
I Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 111: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/111.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal Bath
I Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 112: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/112.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 113: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/113.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican Community
I Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 114: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/114.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groups
I SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 115: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/115.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE experts
I Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 116: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/116.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulators
I Interdisciplinary expertsI Young people
![Page 117: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/117.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary experts
I Young people
![Page 118: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/118.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
I Open issuesI IR behavior of Ghost and Gluon propagatorsI Confinement criteriaI QGVI Simultaneity of Dynamical Symmetry Restoration and
Deconfinement in HICI Nf in QED3
I ExtensionsI Magnetic FieldsI Thermal BathI Other theories
I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people
![Page 119: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/119.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
![Page 120: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/120.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
Enjoy the Conference
Many Thanks
![Page 121: Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and Con nement QED3 Con nement Final Remarks Origin of Mass Lect. 3: Approach Alfredo](https://reader034.vdocuments.net/reader034/viewer/2022043007/5f945e5eb41e5f544230e4d5/html5/thumbnails/121.jpg)
Origin of MassLect. 3: Approach
Alfredo Raya
Contents
DCSB andConfinement
QED3
Confinement
Final Remarks
Final Remarks
Enjoy the Conference
Many Thanks