Forward scattering amplitudes in the imaginary time formalism

TL;DR

This paper explores the connection between loop diagrams and on-shell forward scattering amplitudes in thermal field theories using the imaginary time formalism, enabling efficient calculation of Green's functions at all temperatures.

Contribution

It introduces a method to relate loops to forward scattering amplitudes in thermal field theories, with applications to quantum gravity coupled to scalar matter fields.

Findings

Retarded Green's functions can be expressed in terms of forward scattering amplitudes.

The method applies to planar diagrams at one and two loops.

Facilitates efficient evaluation of thermal Green's functions.

Abstract

We study, in the imaginary time formalism, the relation between loops and on-shell forward scattering tree amplitudes in thermal field theories. This allows for an efficient evaluation, at all temperatures, of Green's functions with causal retarded boundary conditions. We present an application of this relation in quantum gravity coupled to scalar matter fields. We show that at one or two loops, involving planar diagrams, the 1PI retarded thermal Green's functions may respectively be expressed in terms of connected forward scattering tree amplitudes of one or two on-shell particles.