Surveillance on the light-front gauge fixing Lagrangians

TL;DR

This paper introduces a novel approach to gauge fixing in light-front quantum field theory by proposing two Lagrange multipliers, resulting in a complete propagator that is well-defined and exact, despite breaking Lorentz invariance.

Contribution

It presents a new gauge fixing method using two Lagrange multipliers to obtain a full, non-reduced light-front propagator with explicit terms in the Lagrangian.

Findings

Derivation of a complete light-front propagator

Inclusion of $(n ext{·}A)^2$ and $( ext{∂} ext{·}A)^2$ terms in the Lagrangian

The resulting propagator is well-defined and exact despite Lorentz non-invariance

Abstract

In this work we propose two Lagrange multipliers with distinct coefficients for the light-front gauge that leads to the complete (non-reduced) propagator. This is accomplished via $(n\cdot A)^{2}+(\partial \cdot A)^{2}$ terms in the Lagrangian density. These lead to a well-defined and exact though Lorentz non invariant light front propagator.