Pauli-Villars Regularization and Light Front Hamiltonian in (2+1)-dimensional Yang-Mills Theory

TL;DR

This paper introduces a Pauli-Villars regularization scheme for (2+1)-dimensional Yang-Mills theory on the light front, enabling the construction of a renormalized Hamiltonian that maintains equivalence with the conventional formulation.

Contribution

It develops a novel regularization method using extra fields to address renormalization and equivalence issues in light front quantized Yang-Mills theory.

Findings

Regularization scheme successfully restores perturbative equivalence.

Allows construction of a consistent renormalized Hamiltonian.

Provides a framework for nonperturbative studies on the light front.

Abstract

The renormalization problem of (2+1)-dimensional Yang-Mills theory quantized on the light front is considered. Extra fields analogous to those used in Pauli-Villars regularization are introduced to restore perturbative equivalence between such quantized theory and conventional formulation in Lorentz coordinates. These fields also provide necessary ultraviolet regularization to the theory. Obtained results allow to construct renormalized Hamiltonian of the theory on the light front.