Quantum Fields on the Light Front, Formulation in Coordinates close to the Light Front, Lattice Approximation

TL;DR

This paper reviews the quantization of quantum field theories on the Light Front, focusing on Hamiltonian methods, the transition from Lorentzian to Light Front coordinates, and lattice approximations for gauge theories.

Contribution

It provides a comprehensive overview of Light Front quantization, including Hamiltonian approaches and lattice methods for gauge theories, highlighting recent progress and challenges.

Findings

Demonstrates the equivalence of Lorentzian and Light Front formulations.

Discusses the Hamiltonian approach to bound states on the Light Front.

Explores lattice approximations for gauge theories on the Wilson lattice.

Abstract

We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on spacelike hyperplanes) to the theory on the Light Front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice.