Pauli-Villars regularization of field theories on the light front

TL;DR

This paper explores Pauli-Villars regularization for nonperturbative bound state calculations in light-front quantum field theories, aiming to preserve symmetries and facilitate numerical solutions.

Contribution

It introduces a PV regularization scheme tailored for nonperturbative light-front calculations, maintaining symmetries and applying numerical methods to bound-state problems.

Findings

Regularization preserves symmetries in nonperturbative calculations.

Application to QED demonstrates the method's viability.

Bound-state mass eigenvalues can be computed with this approach.

Abstract

Four-dimensional quantum field theories generally require regularization to be well defined. This can be done in various ways, but here we focus on Pauli--Villars (PV) regularization and apply it to nonperturbative calculations of bound states. The philosophy is to introduce enough PV fields to the Lagrangian to regulate the theory perturbatively, including preservation of symmetries, and assume that this is sufficient for the nonperturbative case. The numerical methods usually necessary for nonperturbative bound-state problems are then applied to a finite theory that has the original symmetries. The bound-state problem is formulated as a mass eigenvalue problem in terms of the light-front Hamiltonian. Applications to quantum electrodynamics are discussed.