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

Symplectic quantization of multi-field Generalized Proca electrodynamics