Consistent Non-Minimal Couplings of Massive Higher-Spin Particles

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.

26 pages; to appear in Nuclear Physics B; analyses of consistent backgrounds improved

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• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Cubic interactions of Maxwell-like higher spins
• On the Double Copy for Spinning Matter
• Consistent deformations of free massive field theories in the Stueckelberg formulation
• Higher-Point Positivity
• A Universal Bound on the Strong Coupling Scale of a Gravitationally Coupled Massive Spin-2 Particle
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• Higher-Spin Modes in a Domain-Wall Universe
• Covariant actions and propagators for all spins, masses, and dimensions
• Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• Consistent actions for massive particles interacting with electromagnetism and gravity
• Formalism of gauge invariant curvatures and constructing the cubic vertices for massive spin-3/2 field in AdS_4 space
• General method for including Stueckelberg fields
• The Involutive System of Higher-Spin Equations
• Light-cone AdS/CFT-adapted approach to AdS fields/currents, shadows, and conformal fields
• Revisiting Higher-Spin Gyromagnetic Couplings
• Coulomb problem for classical spinning particle
• Chiral effects in classical spinning gas
• General Backgrounds for higher spin massive particles
• A calculation of the Weyl anomaly for 6D Conformal Higher Spins
• Higher spin fields with reversed spin-statistics relation
• Large-scale messengers from arbitrary spin fields