Symmetry-preserving Loop Regularization and Renormalization of QFTs

TL;DR

This paper introduces a new symmetry-preserving loop regularization method for quantum field theories, which is simple, general, and maintains key symmetries, facilitating higher-loop calculations and renormalization-group analysis.

Contribution

It develops a novel regularization approach that preserves symmetries and can be applied to various quantum field theories without modifying the original formalism or spacetime dimension.

Findings

Simulates features of momentum cutoff, Pauli-Villars, and dimensional regularization.

Applicable to gauge, chiral, supersymmetric, and gravitational theories.

Enables systematic study of renormalization-group evolution and infrared effects.

Abstract

A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the lagrangian formalism or the space-time dimension of original theory. The appearance of characteristic energy scale $M_c$ and sliding energy scale $\mu_s$ offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.