Nonperturbative Pauli-Villars regularization of vacuum polarization in light-front QED

TL;DR

This paper develops a nonperturbative light-front Hamiltonian approach to QED, incorporating Pauli-Villars regularization with two fermion and photon flavors to ensure a finite, Lorentz-invariant photon state.

Contribution

It provides a detailed formulation of Lorentz-gauge light-front QED with two PV fermions and photons, including the constraints for zero photon mass and the complete Hamiltonian.

Findings

Successfully regularized QED using PV fermions and photons.

Derived constraints on PV coupling strengths for a massless photon.

Presented the complete light-front QED Hamiltonian with PV regularization.

Abstract

We continue the development of a nonperturbative light-front Hamiltonian method for the solution of quantum field theories by considering the one-photon eigenstate of Lorentz-gauge QED. The photon state is computed nonperturbatively for a Fock basis with a bare photon state and electron-positron pair states. The calculation is regulated by the inclusion of Pauli-Villars (PV) fermions, with one flavor to make the integrals finite and a second flavor to guarantee a zero mass for the physical photon eigenstate. We compute in detail the constraints on the PV coupling strengths that this zero mass implies. As part of this analysis, we provide the complete Lorentz-gauge light-front QED Hamiltonian with two PV fermion flavors and two PV photon flavors, which will be useful for future work. The need for two PV photons was established previously; the need for two PV fermions is established here.