Pauli-Villars regularization in DLCQ

TL;DR

This paper demonstrates that Pauli-Villars regularization can be effectively combined with discrete light-cone quantization to perform nonperturbative calculations in (3+1)-dimensional field theories, enabling the computation of physical observables.

Contribution

It introduces a method to incorporate Pauli-Villars regularization into DLCQ, allowing nonperturbative solutions with manageable basis sizes and enabling detailed physical quantity calculations.

Findings

Successful combination of Pauli-Villars regularization with DLCQ.

Basis sizes up to 10.5 million used in calculations.

Computed physical quantities like structure functions and form-factor slopes.

Abstract

Calculations in a (3+1)-dimensional model indicate that Pauli-Villars regularization can be combined with discrete light-cone quantization (DLCQ) to solve at least some field theories nonperturbatively. Discrete momentum states of Pauli-Villars particles are included in the Fock basis to automatically generate needed counterterms; the resultant increase in basis size is found acceptable. The Lanczos algorithm is used to extract the lowest massive eigenstate and eigenvalue of the light-cone Hamiltonian, with basis sizes ranging up to 10.5 million. Each Fock-sector wave function is computed in this way, and from these one can obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form-factor slope.