Quantization of Gauge Field Theories on the Front-Form without Gauge Constraints I : The Abelian Case

TL;DR

This paper extends a novel front-form quantization method to Abelian gauge fields, enabling gauge theory quantization along both light-front coordinates without additional gauge constraints, preserving parity explicitly.

Contribution

It introduces a new quantization approach for Abelian gauge theories along both light-front coordinates without requiring gauge fixing conditions.

Findings

Quantization along both $x^+$ and $x^-$ is achieved without extra constraints.

The method preserves parity explicitly.

The approach simplifies gauge field quantization on the light front.

Abstract

Recently, we have proposed a new front-form quantization which treated both the $x^{+}$ and the $x^{-}$ coordinates as front-form 'times.' This quantization was found to preserve parity explicitly. In this paper we extend this construction to local Abelian gauge fields . We quantize this theory using a method proposed originally by Faddeev and Jackiw . We emphasize here the feature that quantizing along both $x^+$ and $x^-$ , gauge theories does not require extra constraints (also known as 'gauge conditions') to determine the solution uniquely.