Soft amplitudes in hot gauge theories: A general analysis

Abstract

A systematic method for the calculation of amplitudes in hot gauge theories is developed. It is necessary to distinguish between hard momenta (of order T) and soft momenta (of order gT). Ordinary perturbation theory applies at hard momenta, but over soft momenta, effective propagators and vertices are required. These effective quantities resum the leading contributions from thermal fluctuations with hard virtual momenta. These “hard thermal loops” arise solely from subdiagrams at one-loop order: they are ultraviolet finite, gauge independent, and satisfy simple Ward identities. To illustrate the method we apply it to the quark and gluon self-energies. Ward identities are used to show that to one-loop order in this effective perturbation expansion, the two-point T -matrix elements constructed from the self-energies are gauge invariant. This proves that to leading order in g, the quark and gluon damping rates are gauge invariant.