Integral representations of thermodynamic 1PI Green functions in the world-line formalism

TL;DR

This paper extends the world-line formalism to finite temperature and chemical potential, providing integral representations for thermodynamic 1PI Green functions and analyzing their non-analytic behavior at zero temperature.

Contribution

It introduces a method to incorporate chemical potential into the world-line formalism and derives integral formulas for thermodynamic Green functions.

Findings

Formulation of the master amplitude at finite temperature and chemical potential

Introduction of a chemical potential for loops in the master formula

Analysis of non-analytic properties at zero temperature with finite chemical potential

Abstract

The issue discussed is a thermodynamic version of the Bern-Kosower master amplitude formula, which contains all necessary one-loop Feynman diagrams. It is demonstrated how the master amplitude at finite values of temperature and chemical potential can be formulated within the framework of the world-line formalism. In particular we present an elegant method how to introduce a chemical potential for a loop in the master formula. Various useful integral formulae for the master amplitude are then obtained. The non-analytic property of the master formula is also derived in the zero temperature limit with the value of chemical potential kept finite.