Real-time propagators at finite temperature and chemical potential

TL;DR

This paper derives simplified spectral representations for bosonic and fermionic propagators at finite temperature and chemical potential, enabling easier loop integral evaluations in real-time field theory.

Contribution

It introduces a new symmetric spectral representation dependent only on analytic functions, facilitating calculations at finite temperature and chemical potential.

Findings

Simplified spectral representations for propagators

Explicit dependence on analytic functions

Easier evaluation of loop integrals with chemical potentials

Abstract

We derive a form of spectral representations for all bosonic and fermionic propagators in the real-time formulation of field theory at finite temperature and chemical potential. Besides being simple and symmetrical between the bosonic and the fermionic types, these representations depend explicitly on analytic functions only. This last property allows a simple evaluation of loop integrals in the energy variables over propagators in this form, even in presence of chemical potentials, which is not possible over their conventional form.