Finite temperature effective actions for double wells

Abstract

The problem of calculating the effective potential for a real scalar field with a double--well potential is a possible preliminary to understanding symmetry breaking phase transitions in the early universe. It is argued here that it is necessary to include multiple saddle points in the path integral formalism and that quadratic source terms are important. The resulting effective action has a well--defined propagator expansion with a positive mass and gives a new way of understanding high temperature expansions, but the results are equally valid at low or zero temperatures.