Thermal Operator Representation of Finite Temperature Graphs II

TL;DR

This paper extends the thermal operator representation to Dirac and gauge fields at finite temperature, showing it works without chemical potential but fails at finite density due to singular contact terms, affecting radiative corrections.

Contribution

It generalizes the thermal operator approach to more complex fields and analyzes its limitations at finite density, revealing new effects on chemical potential screening.

Findings

Thermal operator relates finite and zero temperature graphs without chemical potential.

At finite chemical potential, the factorization is violated by contact terms.

Finite density induces screening effects and renormalization of the chemical potential.

Abstract

Using the mixed space representation, we extend our earlier analysis to the case of Dirac and gauge fields and show that in the absence of a chemical potential, the finite temperature Feynman diagrams can be related to the corresponding zero temperature graphs through a thermal operator. At non-zero chemical potential we show explicitly in the case of the fermion self-energy that such a factorization is violated because of the presence of a singular contact term. Such a temperature dependent term which arises only at finite density and has a quadratic mass singularity cannot be related, through a regular thermal operator, to the fermion self-energy at zero temperature which is infrared finite. Furthermore, we show that the thermal radiative corrections at finite density have a screening effect for the chemical potential leading to a finite renormalization of the potential.