Heat Bath Particle Number Spectrum

TL;DR

This paper develops a systematic method using thermal field theory to calculate the particle number spectrum emitted during scattering processes in a heat bath, demonstrated on a scalar particle model.

Contribution

It introduces a new approach employing the thermal largest-time and Dyson-Schwinger equations for calculating particle spectra at finite temperature.

Findings

Method allows calculation of d<N(ω)>/dω to any order

Applied to a scalar scattering model in a photon-electron heat bath

Shows how to compute changes in photon and electron spectra

Abstract

We calculate the number spectrum of particles radiated during a scattering into a heat bath using the thermal largest-time equation and the Dyson-Schwinger equation. We show how one can systematically calculate {d<N(\omega)>}/{d\omega} to any order using modified real time finite-temperature diagrams. Our approach is demonstrated on a simple model where two scalar particles scatter, within a photon-electron heat bath, into a pair of charged particles and it is shown how to calculate the resulting changes in the number spectra of the photons and electrons.