Thermal Green's Functions from Quantum Mechanical Path Integrals

TL;DR

This paper presents a method to compute thermal Green's functions using quantum mechanical path integrals, simplifying calculations by avoiding loop-momentum integrals and enabling high-temperature expansions.

Contribution

It introduces a path integral approach to evaluate Green's functions in thermal quantum field theory, streamlining calculations and providing a new perspective.

Findings

Avoids loop-momentum integrals in Green's function calculations

Enables high-temperature expansion for all Green's functions simultaneously

Demonstrates the method with a one-loop two-point function in a $b3_6$ model

Abstract

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational approach one avoids the loop-momentum integrals usually encountered in Feynman perturbation theory, although with thermal Green's functions, a discrete sum (over the winding numbers of paths with respect to the circular imaginary time) must be computed. The high-temperature expansion of this sum can be performed for all Green's functions at the same time, and is particularly simple for the static case. The procedure is illustrated by evaluating the two-point function to one-loop order in a $\phi^3_6$ model.