Pauli–villars Regularization in a Discrete Light-cone Model

One of the challenges of using light-cone methods 1,2 to solve nonperturbative problems in field theories such as quantum chromodynamics (QCD) is to develop a nonperturbative regularization and renormalization scheme. Here we discuss a new approach 3,4 based on generalized Pauli–Villars regularization 5 and discretized light-cone quantization (DLCQ). The DLCQ Fock basis is expanded to include momentum states of Pauli–Villars particles which provide the cancelations needed to regulate ultraviolet divergences. The determination of the number of Pauli–Villars particles and of their coupling strengths is done in perturbation theory, where loop integrals are rendered absolutely convergent. We test this approach on a simple model designed to have an analytic solution for the lowest massive state. The model is related to an equal-time model of Greenberg and Schweber, which has also been translated to the light cone by G lazek and Perry.