Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

TL;DR

This paper introduces a renormalization scheme based on Taylor-Lagrange methods that extends singular distributions similarly to Pauli-Villars subtraction but without requiring infinite mass limits, preserving rotational invariance in light-front dynamics.

Contribution

The paper demonstrates how the Taylor-Lagrange renormalization scheme can extend singular distributions akin to Pauli-Villars subtraction without infinite mass limits, applied to light-front dynamics.

Findings

Preserves rotational invariance in light-front calculations.

Provides a finite, consistent extension of singular distributions.

Shows equivalence to Pauli-Villars subtraction without infinite mass limit.

Abstract

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.