$S$-matrix representation of the finite temperature propagator in $\lambda\phi^4$-QFT

TL;DR

This paper derives a finite temperature propagator for a scalar quantum field theory using an S-matrix approach, explicitly separating vacuum and thermal fluctuations, and generalizes the result to higher perturbation orders.

Contribution

It introduces a novel S-matrix representation of the finite temperature propagator in $rac{}{}phi^4$ theory, explicitly separating vacuum and thermal effects.

Findings

Temperature-dependent propagator expressed via scattering amplitudes.

Explicit separation of vacuum and thermal fluctuations.

Generalization of the expression to higher perturbation orders.

Abstract

The two-point Green function of the massive scalar $(3+1)$-quantum field theory with $\lambda\phi^4$ interaction at finite temperature is evaluated up to the 2nd order of perturbation theory. The averaging on the vacuum fluctuations is separated from the averaging on the thermal fluctuations explicitly. As a result, the temperature dependent part of the propagator is expressed through the scattering amplitudes. The obtained expression is generalized for higher orders of perturbation theory.