Light Front Quantization with the Light Cone Gauge

TL;DR

This paper applies the Dirac constraint quantization method to gauge theories on the light front using the light cone gauge, deriving Dirac brackets without eliminating degrees of freedom beforehand, with applications to Yang-Mills theory and superparticles.

Contribution

It introduces a novel approach to light front quantization that retains gauge degrees of freedom during the Dirac procedure, providing new insights into gauge constraint handling.

Findings

Derived explicit Dirac brackets for light front gauge theories

Applied method to Yang-Mills and superparticle models

Demonstrated consistency of gauge constraints without prior elimination

Abstract

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2 + 1 dimensional target space.