Asymptotic regularization method. A constructive approach
Christian Durán Romero, Luis J. Garay, Mercedes Martín-Benito, Rita B. Neves
TLDR
This paper introduces an asymptotic regularization method for QFT divergent integrals, consistently subtracting UV singularities while maintaining symmetries and applying to non-standard theories.
Key contributions
- Presents a new asymptotic regularization method for divergent integrals in quantum field theory.
- Decomposes integrand asymptotics to isolate and consistently subtract UV singularities.
- Maintains covariance and gauge symmetry, applicable to non-standard UV scaling theories.
- Derives non-local logarithmic terms independently of standard renormalization-group flows.
Why it matters
This paper introduces a novel, robust regularization scheme for QFT divergent integrals, ensuring consistent subtraction while preserving fundamental symmetries. It uniquely derives logarithmic terms independent of renormalization-group flows and is applicable to theories with non-standard UV scaling, broadening its utility.
Original 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.
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