Exact bounds on the free energy in QCD

Daniel Zwanziger

Exact bounds on the free energy in QCD

Daniel Zwanziger

Research output: Contribution to journal › Conference article › peer-review

Abstract

We consider the free energy W[J] = Wk(H) of QCD coupled to an external source J_μ^b(x) = H_μ^bcos(k-x), where H_μ^b is, by analogy with spin models, an external "magnetic" field with a color index that is modulated by a plane wave. We report an optimal bound on W_k(H) and an exact asymptotic expression for W_k(H) at large H. They imply confinement of color in the sense that the free energy per unit volume Wk(H)/V and the average magnetization m(k, H) = 1/V ∂W_k(H)/∂H vanish in the limit of constant external field k → 0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) ≠ 0, at k = 0. This would imply a non-analyticity in W_k(H) at k = 0. We also give some general properties of the free energy W(J) for arbitrary J(x). Finally we present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.

Original language	English (US)
Journal	Proceedings of Science
State	Published - 2011
Event	International Workshop on QCD Green's Functions, Confinement and Phenomenology, QCD-TNT 2011 - Trento, Italy Duration: Sep 5 2011 → Sep 9 2011

ASJC Scopus subject areas

General

Cite this

@article{51d658c5359949c8b0512d12aeb1783d,

title = "Exact bounds on the free energy in QCD",

abstract = "We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jμb(x) = Hμbcos(k-x), where Hμb is, by analogy with spin models, an external {"}magnetic{"} field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volume Wk(H)/V and the average magnetization m(k, H) = 1/V ∂Wk(H)/∂H vanish in the limit of constant external field k → 0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) ≠ 0, at k = 0. This would imply a non-analyticity in Wk(H) at k = 0. We also give some general properties of the free energy W(J) for arbitrary J(x). Finally we present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.",

author = "Daniel Zwanziger",

year = "2011",

language = "English (US)",

journal = "Proceedings of Science",

issn = "1824-8039",

publisher = "Sissa Medialab Srl",

note = "International Workshop on QCD Green's Functions, Confinement and Phenomenology, QCD-TNT 2011 ; Conference date: 05-09-2011 Through 09-09-2011",

}

TY - JOUR

T1 - Exact bounds on the free energy in QCD

AU - Zwanziger, Daniel

PY - 2011

Y1 - 2011

N2 - We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jμb(x) = Hμbcos(k-x), where Hμb is, by analogy with spin models, an external "magnetic" field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volume Wk(H)/V and the average magnetization m(k, H) = 1/V ∂Wk(H)/∂H vanish in the limit of constant external field k → 0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) ≠ 0, at k = 0. This would imply a non-analyticity in Wk(H) at k = 0. We also give some general properties of the free energy W(J) for arbitrary J(x). Finally we present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.

AB - We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jμb(x) = Hμbcos(k-x), where Hμb is, by analogy with spin models, an external "magnetic" field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volume Wk(H)/V and the average magnetization m(k, H) = 1/V ∂Wk(H)/∂H vanish in the limit of constant external field k → 0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) ≠ 0, at k = 0. This would imply a non-analyticity in Wk(H) at k = 0. We also give some general properties of the free energy W(J) for arbitrary J(x). Finally we present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.

UR - http://www.scopus.com/inward/record.url?scp=84882979169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882979169&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84882979169

SN - 1824-8039

JO - Proceedings of Science

JF - Proceedings of Science

T2 - International Workshop on QCD Green's Functions, Confinement and Phenomenology, QCD-TNT 2011

Y2 - 5 September 2011 through 9 September 2011

ER -

Exact bounds on the free energy in QCD

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this