Exact solutions to Pauli-Villars-regulated field theories

TL;DR

This paper introduces a class of exactly solvable quantum field theories using Pauli-Villars regularization, providing algorithms for spectrum calculation and insights into light-cone quantization, despite their unphysical ghost states.

Contribution

It presents a new exactly solvable quantum field theory framework with explicit solutions, facilitating analysis of light-cone quantization and perturbative development for physical theories.

Findings

Provided an algorithm to compute the spectrum and eigensolutions.

Illustrated operator solutions in a specific case.

Discussed perturbation theory for physical mass differences.

Abstract

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, we also discuss how perturbation theory in the difference between the masses of the physical and Pauli-Villars particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions.