Hard thermal effective action in QCD through the thermal operator

TL;DR

This paper presents a straightforward derivation of the hard thermal effective action in QCD using the thermal operator applied to zero-temperature Green's functions, highlighting its Lorentz and gauge invariance.

Contribution

It introduces a simple method to derive the hard thermal effective action in QCD by relating Green's functions to forward scattering amplitudes.

Findings

Derivation of the effective action using thermal operator method

Clarification of Lorentz and gauge invariance origins

Connection between Green's functions and scattering amplitudes

Abstract

Through the application of the thermal operator to the zero temperature retarded Green's functions, we derive in a simple way the well known hard thermal effective action in QCD. By relating these functions to forward scattering amplitudes for on-shell particles, this derivation also clarifies the origin of important properties of the hard thermal effective action, such as the manifest Lorentz and gauge invariance of its integrand.