Background field method in the Wilson formulation

TL;DR

This paper introduces a background field method with cutoff regularization for Yang-Mills theory, maintaining gauge invariance and enabling computation of the one-loop beta function.

Contribution

It presents a novel regularization approach within the background field method that preserves gauge invariance in Yang-Mills theories.

Findings

Successfully computed the one-loop beta function.

Maintained explicit gauge invariance during regularization.

Provided a framework for further non-perturbative studies.

Abstract

A cutoff regularization for a pure Yang-Mills theory is implemented within the background field method keeping explicit the gauge invariance of the effective action. The method has been applied to compute the beta function at one loop order.