Quantum electrodynamics in the null-plane causal perturbation theory II

TL;DR

This paper develops a framework for quantum gauge invariance in light-front dynamics within null-plane causal perturbation theory, demonstrating gauge term independence, normalizability, and calculating the electron self-energy in QED.

Contribution

It introduces a complete formulation of quantum gauge invariance in null-plane causal perturbation theory and applies it to QED, showing gauge term independence and normalizability.

Findings

Gauge terms do not contribute to physical S-matrix elements.

The theory is proven to be normalizable.

Electron self-energy is calculated at second order.

Abstract

We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to quantum electrodynamics, showing that the so-called "gauge terms" present in the photon commutation distribution when quantized under the null-plane gauge condition have no contribution in the calculation of the physical S-operator matrix elements at any order. We use this result to prove the normalizability of the theory, and to calculate the electron's self-energy at second order.