Explicit Cutoff Regularization in Coordinate Representation

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.

Automated summary

This paper studies a special type of cutoff regularization in the coordinate representation. It demonstrates how this approach unites various concepts and properties, such as explicit cutoff, spectral representation, homogenization, and covariance. In addition, new formulae are presented to work with the regularization, along with additional calculations of the infrared asymptotics for certain regularized Green's functions in the Yang-Mills theory and Sigma-model.