The Light Front Gauge Propagator: The Status Quo

TL;DR

This paper examines the classical gauge fixing conditions in light front quantization that lead to a three-term gauge field propagator, highlighting differences from the standard two-term form and clarifying their origins.

Contribution

It presents the gauge fixing conditions at the classical level that produce the three-term propagator in light front gauge, clarifying the classical origins of this form.

Findings

Classical gauge fixing conditions can lead to a three-term propagator.

The third term arises from specific gauge fixing choices.

The work clarifies the classical basis for the three-term propagator.

Abstract

At the classical level, the inverse differential operator for the quadratic term in the gauge field Lagrangian density fixed in the light front through the multiplier (nA)^2 yields the standard two term propagator with single unphysical pole of the type (kn)^-1. Upon canonical quantization on the light-front, there emerges a third term of the form (kn^(mu)n^(nu))(kn)^-2. This third term in the propagator has traditionally been dropped on the grounds that is exactly cancelled by the "instantaneous" term in the interaction Hamiltonian in the light-front. Our aim in this work is not to discuss which of the propagators is the correct one, but rather to present at the classical level, the gauge fixing conditions that can lead to the three-term propagator.