Gauge Conditions in the Canonical Hamiltonian Formulation of the Light-Front Quantum Electrodynamics

TL;DR

This paper explores various gauge conditions in the canonical Hamiltonian formulation of light-front quantum electrodynamics, analyzing models with different dimensions and boundary conditions to understand their implications and develop perturbative rules.

Contribution

It systematically studies gauge choices in light-front QED, deriving Hamiltonians and Feynman rules across models with various dimensions and boundary conditions, highlighting their physical differences.

Findings

Derived perturbative Feynman rules for different gauges

Obtained Hamiltonians for all sectors in various models

Analyzed the impact of space-time dimensions on physical meaning

Abstract

We report here the status of different gauge conditions in the canonical formulation of quantum electrodynamics on light-front surfaces. We start with the massive vector fields as pedagogical models where all basic concepts and possible problems manifestly appear. Several gauge choices are considered for both the infinite and the finite volume formulation of massless gauge field electrodynamics. We obtain the perturbative Feynman rules in the first approach and the quantum Hamiltonian for all sectors in the second approach. Different space-time dimensions are discussed in all models where they crucially change the physical meaning. Generally, fermions are considered as the charged matter fields but also one simple 1+1 dimensional model is discussed for scalar fields. Finally the perspectives for further research projects are discussed.