Symplectic quantization of multi-field Generalized Proca electrodynamics

TL;DR

This paper performs symplectic quantization of multi-field Generalized Proca theories, revealing new quantum consistency conditions that restrict which classical models can be successfully quantized.

Contribution

It provides an independent derivation of secondary constraints and uncovers quantum conditions affecting multi-field GP electrodynamics.

Findings

Derived secondary constraint relations for multi-field GP theories.

Discovered quantum consistency conditions limiting quantization.

Showed not all classically consistent theories are quantizable.

Abstract

We explicitly carry out the symplectic quantization of a family of multi-field Generalized Proca (GP) electrodynamics theories. In the process, we provide an independent derivation of the so-called secondary constraint enforcing relations -- consistency conditions that significantly restrict the allowed interactions in multi-field settings already at the classical level. Additionally, we unveil the existence of quantum consistency conditions, which apply in both single- and multi-field GP scenarios. Our newly found conditions imply that not all classically well-defined (multi-)GP theories are amenable to quantization. The extension of our results to the most general multi-GP class is conceptually straightforward, albeit algebraically cumbersome.