Symmetry preserving regularization with a cutoff

TL;DR

This paper introduces a Lorentz and gauge symmetry preserving regularization method in four dimensions using a momentum cutoff, ensuring unambiguous finite terms consistent with dimensional regularization.

Contribution

It presents a novel regularization approach that maintains symmetry properties and provides clear finite results in four-dimensional quantum field theory calculations.

Findings

Finite terms match dimensional regularization results

Method preserves Lorentz and gauge invariance

Unambiguous evaluation of Lorentz index terms

Abstract

A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms carrying Lorentz indices, e.g. proportional to k_{\mu}k_{\nu}. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are unambiguous and agree with the result of dimensional regularization.