Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and...

Origin of MassLect. 3: Approach

Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


Alfredo Raya

IFM-UMSNH

XIII Mexican School of Particles and Fields, San Carlos,Sonora, Mexico.


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


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Contents


A Toy Model: QED3

Confinement in QED3

Final Remarks


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Contents


A Toy Model: QED3

Confinement in QED3

Final Remarks


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Contents


A Toy Model: QED3

Confinement in QED3

Final Remarks


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)


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


S−1F (p) = Z2 S

(0) −1F (p)

+g2 Z1F CF

∫d4k



SF (p) =F (p2)

6p −M(p2)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


S−1F (p) = Z2 S

(0) −1F (p)

+g2 Z1F CF

∫d4k



SF (p) =F (p2)

6p −M(p2)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


Adapted from nucl-th/0007054.


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


g2

∫d4k γµ SF (k) Γν(k, p)∆µν(k − p)

should have an enormous support.

I Strength of interaction g → geff (p)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


g2



I Strength of interaction g → geff (p)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


g2



I The Quark-Gluon Vertex

Adapted from Nucl. Phys. Proc. Suppl. 152 43, (2006).


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


g2



I The Ghost and Gluon Propagators

Adapted from Braz. J. Phys. 37 201 (2007).


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


g2



I The Gluon Propagator is IR finite!

Adapted from PoS LAT2007, 297 (2007).


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD

Confinement can be studied through the IR properties ofGreen’s functions


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


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD






Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD






Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD


Adapted from Nucl. Phys. Proc. Suppl. 152 43, (2006).


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD


Adapted from Braz. J. Phys. 37 201 (2007).


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD


Adapted from PoS LAT2007, 297 (2007).


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).


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QCD

Adapted from J. Phys. G32, R253 (2006).


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

A Toy Model


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


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Why QED3?









I Graphene


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)


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)


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


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Rainbow Truncation



∆(0)µν (q) =

1

q2

(gµν −

qµqνq2

)



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Rainbow Truncation



∆(0)µν (q) =

1

q2

(gµν −

qµqνq2

)



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


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


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


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


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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

∣∣∣∣


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

∣∣∣∣


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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 )


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



M(p) =

∫ ∞0


≈∫ λ


for κ→ 0 and λ→∞

I Using some quadrature rule, we have

M(p) =Nmax∑j=1


=Nmax∑j=1




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



M(p) =

∫ ∞0


≈∫ λ



M(p) =Nmax∑j=1


=Nmax∑j=1




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



M(p) =

∫ ∞0


≈∫ λ



M(p) =Nmax∑j=1


=Nmax∑j=1




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



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


Mk =Nmax∑j=1

wj f (kj ,Mj ; kk ,Mk)


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks




p → pj = kj


M1 =Nmax∑j=1


M2 =Nmax∑j=1


Mk =Nmax∑j=1



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks




p → pj = kj


M1 =Nmax∑j=1


M2 =Nmax∑j=1


Mk =Nmax∑j=1



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks




p → pj = kj


M1 =Nmax∑j=1


M2 =Nmax∑j=1


Mk =Nmax∑j=1



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks




p → pj = kj


M1 =Nmax∑j=1


M2 =Nmax∑j=1


Mk =Nmax∑j=1

wj f (kj ,Mj ; kk ,Mk )


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



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


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


M(p) = 2α

∫d3k

2π2

M(k)

k2 + M2(k)

1

(k − p)2


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


d2

dr2χ(r) +

2

r

d

drχ(r) +

(m2 − 2α

r

)χ(r) = 0


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


M(p) = 2α

∫d3k

2π2

M(k)

k2 + M2(k)

1

(k − p)2


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


d2

dr2χ(r) +

2

r

d

drχ(r) +

(m2 − 2α

r

)χ(r) = 0


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


M(p) = 2α

∫d3k

2π2

M(k)

k2 + M2(k)

1

(k − p)2


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


d2

dr2χ(r) +

2

r

d

drχ(r) +

(m2 − 2α

r

)χ(r) = 0


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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.


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


χ(r) = Ce−mr



M(p) =m3

p2 + m2



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


χ(r) = Ce−mr



M(p) =m3

p2 + m2



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Analytical Insight


χ(r) = Ce−mr



M(p) =m3

p2 + m2



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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


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DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r

)I Quenched approximation G(0) = 1



G(q) =1

1 + e2Nf8q

→ 0 as q → 0




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r




G(q) =1

1 + e2Nf8q

→ 0 as q → 0




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r




G(q) =1

1 + e2Nf8q

→ 0 as q → 0




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r




G(q) =1

1 + e2Nf8q

→ 0 as q → 0




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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r




G(q) =1

1 + e2Nf8q

→ 0 as q → 0


I Including loops of massive fermions, G(0) finite

I Confinement is reinstated


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3


V (r) =e3G(0)

8πln(e2r) + cte +O

(1

r




G(q) =1

1 + e2Nf8q

→ 0 as q → 0




Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Confinement in QED3

Adapted from nucl-th/0007054


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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


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QED3

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This amounts to

G(q)

q2=

1

q2[1 + Π(q)]→ 1

q2 + e2Nf q8


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DCSB andConfinement

QED3

Confinement

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This amounts to

G(q)

q2=

1

q2[1 + Π(q)]→ 1

q2 + e2Nf q8


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DCSB andConfinement

QED3

Confinement

Final Remarks


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

]


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DCSB andConfinement

QED3

Confinement

Final Remarks



M(p) =1

2π2p

∫ ∞0

dkkM(k)

k2 + M2(k)ln

[k + p + Nf /8

|k − p|+ Nf /8

]


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



M(p) =1

2π2p

∫ ∞0

dkkM(k)

k2 + M2(k)ln

[k + p + Nf /8

|k − p|+ Nf /8

]


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


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)


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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks





e2



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks





e2



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Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


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)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


I Ward identity

I (k − p)νΓν = S−1F (k)− S−1

F (p)


I We end up with

M(p) ∼∫

dkF (k)M(k)

k2 + M2(k)

(F (k),F (p))

1 + Π(k − p)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


I Ward identity

I (k − p)νΓν = S−1F (k)− S−1

F (p)


I We end up with

M(p) ∼∫

dkF (k)M(k)

k2 + M2(k)

(F (k),F (p))

1 + Π(k − p)


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


I Ward identity

I (k − p)νΓν = S−1F (k)− S−1

F (p)


I We end up with

M(p) ∼∫

dkF (k)M(k)

k2 + M2(k)

(F (k),F (p))

1 + Π(k − p)


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


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks


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)


Π(ζq) = ζ−(1+δ)Π(q)

I Combining results

M(ζp) = M(p)!!



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks



identityI F (p) should be an homogeneous function of momentum

in the IR :F (ζp) = ζδF (p)


Π(ζq) = ζ−(1+δ)Π(q)

I Combining results

M(ζp) = M(p)!!



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks






Π(ζq) = ζ−(1+δ)Π(q)

I Combining results

M(ζp) = M(p)!!



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks






Π(ζq) = ζ−(1+δ)Π(q)

I Combining results

M(ζp) = M(p)!!



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks






Π(ζq) = ζ−(1+δ)Π(q)

I Combining results

M(ζp) = M(p)!!



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

DMG and Confinement


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

DMG and Confinement


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


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks


I Dynamical Chiral Symmetry Breaking

I Confinement



I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks



I Schwinger-Dyson equations

I Natural platform to study non-perturbative phenomenaI Infinite tower of relations among Green’s functions


I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks



I Schwinger-Dyson equationsI Natural platform to study non-perturbative phenomena

I Infinite tower of relations among Green’s functions


I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Compare against lattice simulations

I Heavy Ion CollisionsI RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHIC

I LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC

I Condensed Matter Systems

I SuperconductivityI Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC

I Condensed Matter SystemsI Superconductivity

I Graphene


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks





I RHICI LHC



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


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





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




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




Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks



I ExtensionsI Magnetic Fields

I Thermal BathI Other theories



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks



I ExtensionsI Magnetic FieldsI Thermal Bath

I Other theories



Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks






Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Mexican Community

I Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Mexican CommunityI Working groups

I SDE expertsI Lattice simulatorsI Interdisciplinary expertsI Young people


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Mexican CommunityI Working groupsI SDE experts

I Lattice simulatorsI Interdisciplinary expertsI Young people


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Mexican CommunityI Working groupsI SDE expertsI Lattice simulators

I Interdisciplinary expertsI Young people


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks




I Mexican CommunityI Working groupsI SDE expertsI Lattice simulatorsI Interdisciplinary experts

I Young people


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks






Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks

Enjoy the Conference

Many Thanks


Alfredo Raya

Contents

DCSB andConfinement

QED3

Confinement

Final Remarks

Final Remarks

Enjoy the Conference

Many Thanks

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Origin of Mass Lect. 3: Approach · Origin of Mass Lect. 3: Approach Alfredo Raya Contents DCSB and...

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