On a criterion for a cutoff regularization in the coordinate representation

Abstract

The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not empty. As an example, an explicit function is presented. It is proved by explicit construction that there are functions satisfying the criterion in a stronger formulation.

LaTeX, 8 pages, 1 figure. Firstly appeared in Russian, March 5, 2024. Compared to the Russian version, some comments and minor corrections have been added. The forgotten imaginary unit in the Fourier transform has also been restored. See https://www.pdmi.ras.ru/preprint/2024/24-04.html

References in corpus (2)

• Quantum equation of motion and two-loop cutoff renormalization for ${\varphi }^3$ model
• Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization

Cited by in corpus (1)

• Summation of power singularities