We revisit the problem of consistent free propagation of higher-spin fields in nontrivial backgrounds, focusing on symmetric tensor(-spinor)s. The Fierz-Pauli equations for massive fields in flat space form an involutive system, whose algebraic consistency owes to certain gauge identities. The zero mass limit of the former leads directly to massless higher-spin equations in the transverse-traceless gauge, where both the field and the gauge parameter have their respective involutive systems and gauge identities. In nontrivial backgrounds, it is the preservation of these gauge identities and symmetries that ensures the correct number of propagating degrees of freedom. With this approach we find consistent sets of equations for massive and massless higher-spin bosons and fermions in certain gravitational/electromagnetic backgrounds. We also present the involutive system of partially massless fields, and give an explicit form of their gauge transformations. We consider the Lie superalgebra of the operators on symmetric tensor(-spinor)s in flat space, and show that in AdS space the algebra closes nonlinearly and requires a central extension.

我们重新讨论了在非平凡背景下高自旋场的一致自由传播的问题，重点是对称张量（自旋）。平面空间中大质量场的Fierz-Pauli方程形成了一个对合系统，其代数一致性归因于某些量表恒等式。前者的零质量极限直接导致了无轨横向测量仪中无质量的高自旋方程，其中场和测量仪参数都有各自的对合系统和测量仪身份。在非平凡的背景下，正是这些量规标识和对称性的保存确保了正确的传播自由度数。通过这种方法，我们发现了在某些重力/电磁背景下，质量无质量的高自旋玻色子和费米子具有一致的方程组。我们还介绍了部分无质量场的对合系统，并给出了其规范变换的明确形式。我们考虑了平面空间中对称张量（-spinor）上算子的李超代数，并表明在AdS空间中，代数非线性地闭合并且需要中心扩展。