The Electromagnetic and Proca Fields Revisited: a Unified Quantization

TL;DR

This paper presents a novel approach to quantizing electromagnetic and Proca fields by reformulating gauge transformations as trajectories generated by vector fields, enabling a unified quantization without BRST parameters.

Contribution

It introduces a new method for gauge transformations as trajectories with null Noether invariants, allowing unified quantization of electromagnetic and Proca fields without BRST-like parameters.

Findings

Unified quantization of electromagnetic and Proca fields achieved.

Gauge transformations interpreted as trajectories with dynamical parameters.

Elimination of the need for BRST-like parameters in quantization.

Abstract

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, $A_{\mu}(x)\rightarrow A_{\mu}(x)+\partial_{\mu}\varphi(x)$, into a group law. In this paper it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, $U(1)(\vec{x},t)$, acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.