Gauge and Poincare' Invariant Regularization and Hopf Symmetries

TL;DR

This paper introduces a Poincare' invariant regularization method for gauge quantum field theories using a modified product of fields, resulting in a new Hopf algebra structure that preserves symmetries throughout the regularization process.

Contribution

It develops a symmetry-preserving regularization approach based on a deformed product, leading to a novel Hopf algebra structure in gauge theories.

Findings

Regularization preserves all symmetries at each stage.

Introduces a new Hopf algebra with deformed co-structures.

Ensures gauge invariance in the regularized theory.

Abstract

We consider the regularization of a gauge quantum field theory following a modification of the Polchinski proof based on the introduction of a cutoff function. We work with a Poincare' invariant deformation of the ordinary point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and Sadooghi, and show that it yields, through a limiting procedure of the cutoff functions, to a regularized theory, preserving all symmetries at every stage. The new gauge symmetry yields a new Hopf algebra with deformed co-structures, which is inequivalent to the standard one.