Hard thermal effective action in QCD through the thermal operator

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.