Consistent non-minimal couplings of massive higher-spin particles

The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach avoids this difficulty, but fails to ensure light-cone propagation and becomes very cumbersome. In this paper, we take an alternative route—the involutive form of the equations and constraints—to guarantee their algebraic consistency. This approach enormously simplifies the search for consistent interactions, now seen as deformations of the involutive system, by keeping manifest the causal propagation of the correct number of degrees of freedom. We consider massive particles of arbitrary integer spin in electromagnetic and gravitational backgrounds to find their possible non-minimal local couplings. Apart from easily reproducing some well-known results, we find restrictions on the backgrounds for consistent propagation of such a particle in isolation. The results can be altered by non-local interactions that may arise from additional massive states in the interacting theory.