One-loop thermal field theory in three dimensions.

Abstract

We consider thermal field theory in three dimensions to one-loop order using the quantum-mechanical path integral. Upon reexpressing the sum over winding numbers by the Poisson resummation formula, and then using an integral representation for the sum, we find that the temperature dependence of the generating functional can be expressed in closed form at one-loop order. In a pure scalar theory, only Green{close_quote}s functions with two external vertices have temperature dependence, while, in a gauge theory, one has temperature dependence only if there are two, three, or four external spatial vectors in the static limit. The {eta} function that occurs when one considers a quantum spinor field in a background gauge field vanishes for all temperatures larger than zero. {copyright} {ital 1996 The American Physical Society.}