The Indispensability of Ghost Fields in the Light-Cone Gauge Quantization of Gauge Fields

TL;DR

This paper demonstrates the essential role of ghost fields in light-cone gauge quantization of gauge fields, introducing a new canonical formulation that simplifies the process and clarifies the structure of propagators.

Contribution

It develops a constraint-free canonical formulation of the electromagnetic field in auxiliary coordinates, enabling straightforward light-cone gauge quantization and analysis of ghost fields.

Findings

Ghost fields are crucial for well-defined propagators.

A new canonical formulation avoids constrained systems.

The Mandelstam-Leibbrandt propagator form is derived in temporal gauge.

Abstract

We continue McCartor and Robertson's recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore to circumvent dealing with constrained systems, we construct the temporal gauge canonical formulation of the free electromagnetic field in auxiliary coordinates $x^{\mu}=(x^-,x^+,x^1,x^2)$ where $x^-=x^0 cos{\theta}-x^3 sin{\theta}, x^+=x^0 sin{\theta}+x^3 cos{\theta}$ and $x^-$ plays the role of time. In so doing we can quantize the fields canonically without any constraints, unambiguously introduce "static ghost fields" as residual gauge degrees of freedom and construct the light-cone gauge solution in the light-cone representation by simply taking the light-cone limit (${\theta}\to \pi/4$). As a by product we find that, with a suitable choice of vacuum the Mandelstam-Leibbrandt form of the propagator can be derived in the ${\theta}=0$ case (the temporal gauge formulation in the equal-time representation).