Consistent Non-Minimal Couplings of Massive Higher-Spin Particles

TL;DR

This work tackles the problem of achieving consistent interactions for massive higher-spin particles by employing the involutive form of the equations and constraints, ensuring algebraic consistency and causal propagation of the correct DoFs. Using a perturbative deformation framework, the authors derive non-minimal electromagnetic and gravitational couplings for arbitrary spin, identifying background conditions that guarantee locality and DoF preservation. They establish universal results—$g=2$ for the gyromagnetic ratio and $h=1$ for the gravimagnetic ratio—in the local isolated case, while showing how non-locality or additional massive states can modify these values. The findings illuminate precise background requirements and demonstrate the practicality of the involutive approach as a simpler alternative to Lagrangian methods, with potential implications for string theory and higher-spin phenomenology.

Abstract

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.