Symplectic quantization of multifield generalized Proca electrodynamics

Abstract

We explicitly carry out the symplectic quantization of a family of multifield 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 multifield settings already at the classical level. Additionally, we unveil the existence of quantum consistency conditions, which apply in both single- and multifield 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.