On the correspondence between Light-Front Hamiltonian approach and Lorentz-covariant formulation for Quantum Gauge Theory

TL;DR

This paper establishes the equivalence between Light-Front Hamiltonian and Lorentz-covariant formulations in gauge theories, specifically for QED(1+1) and QCD(3+1), through bosonization and a novel regularization method.

Contribution

It provides a method to restore equivalence between formulations for gauge theories, including a bosonization approach for QED and a regularization scheme for QCD.

Findings

LF Hamiltonian reproduces Lorentz-covariant results for QED(1+1)

Restores equivalence for QCD(3+1) with finite counterterms

Perturbative equivalence achieved to all orders in QED

Abstract

The problem of the restoring of the equivalence between Light-Front (LF) Hamiltonian and conventional Lorentz-covariant formulations of gauge theory is solved for QED(1+1) and (perturbatively to all orders) for QCD(3+1). For QED(1+1) the LF Hamiltonian is constructed which reproduces the results of Lorentz-covariant theory. This is achieved by bosonization of the model and by analysing the resulting bosonic theory to all orders in the fermion mass. For QCD(3+1) we describe nonstandard regularization that allows to restore mentioned equivalence with finite number of counterterms in LF Hamiltonian.