Asymptotic regularization method. A constructive approach

TL;DR

This paper presents a new asymptotic regularization method for divergent integrals in quantum field theory, which isolates UV singularities and maintains symmetries, applicable to various theories.

Contribution

The paper introduces a constructive asymptotic regularization scheme that handles divergences based on integrand structure, independent of standard power counting.

Findings

The method isolates UV divergences while preserving covariance and gauge symmetry.

Renormalized quantities show non-local logarithmic dependence determined by UV asymptotics.

Applicable to theories with modified dispersion relations and non-standard UV scaling.

Abstract

We introduce a new regularization scheme for divergent integrals in quantum field theory. The framework is based on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive UV singularities and those that remain finite. This asymptotic regularization method isolates the genuinely singular sector and enables a consistent subtraction of divergences while maintaining covariance and gauge symmetry. In single-scale theories, we show that the renormalized quantities exhibit a non-local logarithmic dependence uniquely determined by the UV asymptotics, offering a derivation of logarithmic terms that is independent of standard renormalization-group flows. Because it relies only on asymptotic structure rather than on standard relativistic power counting, the method is naturally applicable to theories with modified dispersion relations and non-standard UV scaling. Although formulated here for ultraviolet divergences, the underlying strategy extends straightforwardly to infrared singularities.