Singularity Problem for Interacting Massive Vectors.

Interacting massive spin-1 fields have been widely used in cosmology and particle physics. We obtain a new condition on the validity of the classical limit of these theories related to the nontrivial constraints that exist for vector field components. A violation of this consistency condition causes a singularity in the time derivative of the auxiliary component and could impact, for example, the field's cosmic history and superradiance around black holes. We show that gauge-invariant interactions are generally safe from this problem, even though the mass term explicitly breaks the gauge symmetry. Such restrictions for interactions are expected to exist generically in many other nontrivially constrained systems.