Scattering amplitude and shift in self-energy in medium

TL;DR

This paper presents two straightforward proofs for the first-order virial expansion of a particle's self-energy in a medium, applicable at finite temperature and chemical potential, using operator and diagrammatic methods.

Contribution

It introduces two simple, complementary proofs for the first-order virial expansion of self-energy in medium, enhancing theoretical understanding.

Findings

Validates the virial expansion approach for self-energy in medium

Provides diagrammatic and operator-based proofs

Applicable at finite temperature and chemical potential

Abstract

Two simple proofs are presented for the first order virial expansion of the self-energy of a particle moving through a medium, characterised by temperature and/or chemical potential(s). One is based on the virial expansion of the self-energy operator itself, while the other is on the analysis of its Feynman diagrams in configuration space.