Hard thermal effective actions in the Schwinger formulation

TL;DR

This paper derives properties of hard thermal effective actions in gauge theories using Schwinger's proper time formulation, highlighting the role of conserved generalized energies and momenta in understanding their non-local behavior.

Contribution

It introduces a set of conserved, non-local generalized energies and momenta that simplify the derivation of hard thermal effective actions in gauge theories.

Findings

Generalized energies generate non-local behavior of effective actions.

Effective actions become local in the static limit.

Conserved quantities relate to gauge invariant potentials.

Abstract

We derive the properties of hard thermal effective actions in gauge theories from the point of view of Schwinger's proper time formulation. This analysis is simplified by introducing a set of generalized energy and momenta which are conserved and are non-local in general. These constants of motion, which embody energy-momentum exchanges between the fields and the particles along their trajectories, can be related to a class of gauge invariant or covariant potentials in the hard thermal regime. We show that in this regime the generalized energy, which is non-local in general, generates the relevant non-local behavior of hard thermal effective actions which become local only in the static limit.