Explicit Cutoff Regularization in Coordinate Representation

TL;DR

This paper introduces a specific cutoff regularization method in coordinate space that unifies various concepts and provides new formulas and calculations for Green's functions in Yang-Mills and Sigma-model theories.

Contribution

It presents a novel cutoff regularization approach in coordinate representation, linking multiple theoretical concepts and offering new computational formulas.

Findings

Unified regularization approach connecting multiple concepts.

New formulas for regularized Green's functions.

Infrared asymptotics calculations in Yang-Mills and Sigma-models.

Abstract

In this paper, we study a special type of cutoff regularization in the coordinate representation. We show how this approach unites such concepts and properties as an explicit cut, a spectral representation, a homogenization, and a covariance. Besides that, we present new formulae to work with the regularization and give additional calculations of the infrared asymptotics for some regularized Green's functions, appearing in the pure four-dimensional Yang-Mills theory and in the standard two-dimensional Sigma-model.