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.

中文翻译：

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交互海量向量的奇点问题

相互作用的大质量自旋 1 场已广泛用于宇宙学和粒子物理学。我们获得了关于这些理论的经典极限有效性的新条件，这些理论与矢量场分量存在的非平凡约束有关。违反这种一致性条件会导致辅助分量的时间导数出现奇点，并可能影响场的宇宙历史和黑洞周围的超辐射等。我们表明，规范不变的相互作用通常不会出现这个问题，即使质量项明确破坏了规范对称性。预计这种交互限制一般存在于许多其他非平凡约束系统中。