QCD Pressure and the Trace Anomaly

TL;DR

This paper derives exact relations between QCD thermal pressure and trace anomaly, proving their equivalence in equilibrium and providing a Dyson-resummed formula to address infrared issues in perturbation theory.

Contribution

It introduces new exact relations linking QCD pressure and trace anomaly, and presents a Dyson-resummed expression for pressure in the temporal axial gauge.

Findings

Proves the equivalence of thermodynamic and hydrodynamic pressure in equilibrium.

Derives a Dyson-resummed formula for thermal pressure.

Addresses infrared problems in perturbative QCD calculations.

Abstract

Exact relations between the QCD thermal pressure and the trace anomaly are derived. These are used, first, to prove the equivalence of the thermodynamic and the hydrodynamic pressure in equilibrium in the presence of the trace anomaly, closing a gap in previous arguments. Second, in the temporal axial gauge a formula is derived which expresses the thermal pressure in terms of a Dyson-resummed two-point function. This overcomes the infrared problems encountered in the conventional perturbation-theory approach.