Axial Couplings on the World-Line

TL;DR

This paper develops a world-line approach to compute fermionic one-loop effective actions with various couplings, successfully reproducing known results like the chiral anomaly, and validating the method against standard field theory calculations.

Contribution

It introduces a novel world-line representation for fermionic effective actions with axial and other couplings, enabling new computational techniques.

Findings

Reproduces the chiral anomaly using the world-line method

Matches results from standard field theory for scattering amplitudes

Provides a new framework for fermionic effective actions

Abstract

We construct a world-line representation for the fermionic one-loop effective action with axial and also vector, scalar, and pseudo-scalar couplings. We use this expression to compute a few selected scattering amplitudes. These allow us to verify that our method yields the same results as standard field theory. In particular, we are able to reproduce the chiral anomaly. Our starting point is the second-order formulation for the Dirac fermion. We translate the second order expressions into a world-line action.