The mass renormalization of nonperturbative light-front Hamiltonian theory: An illustration using truncated, Pauli-Villars-regulated Yukawa interactions

TL;DR

This paper presents an analytic, nonperturbative approach to Yukawa theory using light-front quantization with Pauli-Villars regularization, focusing on the one-fermion sector and analyzing wave function features and mass limits.

Contribution

It introduces a nonperturbative, analytic solution to Yukawa theory with Pauli-Villars regularization, neglecting pair creation and limiting bosonic constituents.

Findings

Wave function endpoint behavior analyzed

Spin and orbital angular momentum content characterized

Infinite Pauli-Villars mass limit examined

Abstract

We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli-Villars mass receives special scrutiny.