Asymptotic transition from Fourier series to integrals in LGT

TL;DR

This paper investigates the transition from Fourier series to integrals in lattice gauge theory, highlighting potential errors and ambiguities, and proposes methods to correct and eliminate these ambiguities under certain conditions.

Contribution

It introduces a detailed analysis of ambiguities in the asymptotic transition from Fourier series to integrals and provides a correction method with specific conditions to avoid these issues.

Findings

Identifies sources of errors and ambiguities in the transition process.

Establishes conditions under which ambiguities do not occur.

Proposes a correction method to address potential ambiguities.

Abstract

It is shown that in asymptotic transition from Fourier series to integrals an error and ambiguity may arise. Ambiguity reduces to a possibility of addition of some distribution to the result. Properties of such distributions are studied and conditions are established under which ambiguity doesn't arise. Method for correction computation is suggested and conditions for correction turning to zero are specified.