标题： 广义多Proca场 显示英文标题

标题： Generalized multi-Proca fields

摘要： 我们将之前关于Proca场健康导数自相互作用的结果推广到一组有质量矢量场的情况。我们获得了非规范不变的矢量场导数自相互作用，这些相互作用保持了适当的传播自由度数量。鉴于潜在的宇宙学应用，我们限制于具有内部旋转对称性的相互作用。我们通过系统地按场的导数阶次构造，并利用反对称的Levi-Civita张量来实现这一点。然后我们将此与单个矢量场的情况进行比较，表明这些相互作用可以大致分为两类：一类是从广义Proca项的直接扩展而来；另一类是真正的多Proca相互作用，在单Proca情况下没有对应物。我们还讨论了相互作用的弯曲时空版本，以包含必要的非最小耦合到引力的项。最后，我们探讨了宇宙学应用，并展示了存在三种不同的矢量场构型可导致各向同性解。其中两种已在文献中被考虑过，而第三种代表前两者的组合，是新的，并提供了未探索的宇宙学场景。 显示英文摘要

摘要： We extend previous results on healthy derivative self-interactions for a Proca field to the case of a set of massive vector fields. We obtain non-gauge invariant derivative self-interactions for the vector fields that maintain the appropriate number of propagating degrees of freedom. In view of the potential cosmological applications, we restrict to interactions with an internal rotational symmetry. We provide a systematical construction order by order in derivatives of the fields and making use of the antisymmetric Levi-Civita tensor. We then compare with the one single vector field case and show that the interactions can be broadly divided into two groups, namely the ones obtained from a direct extension of the generalized Proca terms and genuine multi-Proca interactions with no correspondence in the single Proca case. We also discuss the curved spacetime version of the interactions to include the necessary non-minimal couplings to gravity. Finally, we explore the cosmological applications and show that there are three different vector fields configurations giving rise to isotropic solutions. Two of them have already been considered in the literature and the third one, representing a combination of the first two, is new and offers unexplored cosmological scenarios.