On Gauge-Invariant Entire-Function Regulators and UV Finiteness in NonLocal Quantum Field Theory

TL;DR

This paper demonstrates that gauge-invariant entire function regulators in nonlocal quantum field theory provide exponential UV damping in loop integrals without extra poles, ensuring gauge covariance and finiteness.

Contribution

It offers a gauge covariant justification for using entire function regulators in nonlocal quantum field theory, clarifying their role in UV finiteness.

Findings

Entire function regulators produce exponential UV damping in Minkowski momentum space.

The approach preserves gauge covariance without introducing additional poles or branch cuts.

Analysis confirms the regulators' effectiveness in ensuring UV finiteness in nonlocal QFT.

Abstract

In this paper we clarify the status of gauge invariant entire function regulators in NonLocal Quantum Field Theory, in this the regulator is implemented as an entire function of the covariant Laplace--Beltrami operator. Working in the background-field formalism and expanding around flat, trivial backgrounds, we show that plane waves diagonalize the d'Alembertian so that the entire function reduces to a multiplicative form factor in Minkowski momentum space. After Wick rotation to the Euclidean axis, this produces exponential ultraviolet damping in loop integrals without introducing additional poles or branch cuts. Our analysis provides a gauge covariant justification for the use of entire function regulators in nonlocal quantum field theory.