Quantum Field Theory in Light-Front coordinates

TL;DR

This paper reviews the canonical formulation of quantum field theory on the Light Front, addressing the construction of the LF Hamiltonian, regularization methods, and their implications for gauge invariance and constraints.

Contribution

It introduces a gauge-invariant regularization approach using transverse lattice and boundary conditions, simplifying the LF canonical formalism and constraints handling.

Findings

LF Hamiltonian construction methods analyzed

Gauge-invariant regularization via transverse lattice proposed

Simplification of constraints in LF formalism achieved

Abstract

Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe possible ways of solving this problem: (a) the limiting transition from the equal-time Hamiltonian in a fastly moving Lorentz frame to LF Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling constant and usual Lorentz-covariant Feynman perturbation theory. Gauge invariant regularization of LF Hamiltonian via introducing a lattice in transverse coordinates and imposing periodic boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|< L$ is considered. We find that LF canonical formalism for this regularization avoid usual most complicated constraints connecting zero and nonzero modes of gauge fields.