The Light-Front Hamiltonian formalism for two-dimensional Quantum Electrodynamics equivalent to the Lorentz-covariant approach

TL;DR

This paper constructs a light-front Hamiltonian for two-dimensional quantum electrodynamics that reproduces Lorentz-covariant results, incorporating a counterterm linked to the fermion condensate and ensuring consistency across all orders of perturbation theory.

Contribution

It introduces a novel light-front Hamiltonian with a specific counterterm that aligns with Lorentz-covariant results in 2D QED, accounting for fermion condensate effects.

Findings

The Hamiltonian reproduces Lorentz-covariant results in all orders.

The counterterm depends on the fermion condensate in the heta-vacuum.

The counterterm coefficient is finite and linearly related to the condensate for small fermion mass.

Abstract

A light-front Hamiltonian reproducing the results of two-dimensional quantum electrodynamics in the Lorentz coordinates is constructed using the bosonization procedure and an analysis of the bosonic perturbation theory in all orders in the fermion mass. The resulting Hamiltonian involves a supplementary counterterm in addition to the usual terms appearing in the naive light-front quantization. This term is proportional to a linear combination of zeroth fermion modes (which are multiplied by a factor compensating the charge and fermion number). The coefficient of the counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the \theta-vacuum, and is linear in this value for a small fermion mass.