Thermal Green's Functions from Quantum Mechanical Path Integrals II: Inclusion of Fermions

TL;DR

This paper extends the quantum mechanical path integral approach to include fermionic fields, enabling the calculation of thermal Green's functions with fermions in a unified framework.

Contribution

It introduces a method to incorporate fermionic boundary conditions into path integrals for thermal Green's functions, expanding previous bosonic-only techniques.

Findings

Successfully applied to scalar and spinor self-energies

Unified treatment of bosonic and fermionic Green's functions

Demonstrated in a Yukawa coupling model

Abstract

In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum mechanical path integral. In this paper we extend this method to include fermionic fields. A particular problem is posed by Green's functions with external fermionic lines, where the different boundary conditions of bosons and fermions in imaginary time have to be accommodated within one path integral expression. The general procedure is worked out in the example of scalar and spinor self-energies in a simple model with a Yukawa coupling of a scalar to a Majorana spinor.