QCD Pressure at Two Loops in the Temporal Gauge

TL;DR

This paper calculates the two-loop thermodynamic pressure in QCD using zeta function methods and a specific gauge prescription, confirming gauge independence of the result.

Contribution

It introduces a novel application of zeta functions and a special gauge prescription to evaluate QCD pressure at two loops, providing a gauge-independent result.

Findings

Two-loop pure-gauge pressure in QCD is proportional to g^2N_cN_gT^4.

The calculated pressure agrees with the Feynman gauge result.

Method confirms gauge independence of the thermodynamic pressure.

Abstract

We apply the method of \underline{zeta} functions, together with the $n_\mu^*$-prescription for the temporal gauge, to evaluate the thermodynamic pressure in QCD at finite temperature $T$. Working in the imaginary-time formalism and employing a special version of the unified-gauge prescription, we show that the pure-gauge contribution to the pressure at two loops is given by $P_2^{\mbox{{\scriptsize gauge}}} = -(g^2/144)N_cN_gT^4$, where $N_c$ and $N_g$ denote the number of colours and gluons, respectively. This result agrees with the value in the Feynman gauge.