Worldline Path Integrals for Fermions with General Couplings

TL;DR

This paper develops a worldline path integral framework for Dirac fermions interacting with complex background fields, maintaining chiral gauge invariance and enabling advanced quantum field theory calculations.

Contribution

It introduces a novel worldline path integral representation for fermions coupled to general background fields, including internal degrees of freedom as worldline fermions.

Findings

Provides a manifestly chiral gauge invariant formulation

Enables calculation of effective actions with complex couplings

Extends the worldline formalism to general fermionic interactions

Abstract

We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance.