Manifestly gauge-covariant representation of scalar and fermion propagators

TL;DR

This paper introduces a gauge-covariant representation of scalar and fermion propagators in weak gauge fields, simplifying calculations and clarifying gauge properties, with implications for amplitude computation and anomaly analysis.

Contribution

It presents a novel gauge-covariant form of propagators that reduces diagram complexity and aids in deriving counterterms and anomalies.

Findings

Facilitates gauge-covariant amplitude calculations

Reduces the number of Feynman diagrams needed

Provides a scheme-independent way to express counterterms

Abstract

A new way to write the massive scalar and fermion propagators on a background of a weak gauge field is presented. They are written in a form that is manifestly gauge-covariant up to several additional terms that can be written as boundary terms in momentum space. These additional terms violate Ward-Takahashi identities and need to be renormalized by appropriate counterterms if the complete theory is to be gauge-covariant. This form makes it possible to calculate many amplitudes in a manifestly gauge-covariant way (at the same time reducing the number of Feynman diagrams). It also allows to express some counterterms in a way independent of the regularization scheme and provides an easy way to derive the anomalous term affecting the chiral current conservation.