A Dual Path Integral Representation for Finite Temperature Quantum Field Theory

TL;DR

This paper introduces a dual path integral formulation for finite temperature quantum field theory by imposing Matsubara periodicity constraints via auxiliary fields, resulting in a lower-dimensional representation with a classical-like measure.

Contribution

It presents a novel dual path integral approach that simplifies finite temperature quantum field calculations by reducing the dimensionality and maintaining a classical measure.

Findings

Fields in the dual representation live in one less dimension.

The quantum partition function has a measure identical to the classical case.

The action in the dual representation is spatially nonlocal.

Abstract

We impose the periodicity conditions corresponding to the Matsubara formalism for Thermal Field Theory as constraints in the imaginary time path integral. These constraints are introduced by means of time-independent auxiliary fields which, by integration of the original variables, become dynamical fields in the resulting `dual' representation for the theory. This alternative representation has the appealing property of involving fields which live in one dimension less than the original ones, with a quantum partition function whose integration measure is identical to the one of its classical counterpart, albeit with a different (spatially nonlocal) action.