Pauli--Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization

TL;DR

This paper introduces a nonperturbative renormalization method for light-cone Hamiltonian theories using generalized Pauli--Villars regulators, ensuring Lorentz invariance and finite results, demonstrated through Yukawa theory and a 3+1 dimensional model.

Contribution

It presents a novel nonperturbative renormalization approach employing Pauli--Villars regulators within discretized light-cone quantization, maintaining symmetries and enabling numerical solutions.

Findings

Numerical results agree well with analytic solutions.

The method successfully renders theories finite and symmetric.

Nonperturbative solutions are obtained for complex models.

Abstract

We propose a solution to the problem of renormalizing light-cone Hamiltonian theories while maintaining Lorentz invariance and other symmetries. The method uses generalized Pauli--Villars regulators to render the theory finite. We discuss the method in the context of Yukawa theory at one loop and for a soluble model in 3+1 dimensions. The model is studied nonperturbatively. Numerical results obtained with use of discretized light-cone quantization, special integration weighting factors, and the complex symmetric Lanczos diagonalization algorithm compare well with the analytic answers.