Gauge invariance and generalised $\eta$ regularisation

TL;DR

This paper extends the $ta$ regularisation method to systematically analyze gauge-invariant regularisation schemes in quantum field theory, recovering known methods and exploring anomalies in chiral theories.

Contribution

It introduces a generalized $ta$ regularisation framework that unifies various gauge-invariant regularisation schemes and addresses anomalies in chiral theories.

Findings

Recovered known regularisation schemes like dimensional and denominator regularisations.

Developed a systematic approach to study gauge consistency conditions.

Provided insights into anomalies in chiral gauge theories.

Abstract

We generalise the $\eta$ regularisation scheme in order to develop a framework for systematically studying regularisation of loops in quantum field theory. This allows us to "solve" a set of gauge consistency conditions for families of gauge invariant regularisation schemes. We recover several known examples such as dimensional and denominator regularisations, as well as some more general solutions. We also study anomalies in chiral theories in order to carefully describe how our formalism should be properly implemented.