Cubic interaction vertices in higher spin theories

Abstract

Based purely on symmetry considerations, we derive the following result: in momentum space, the cubic term in the Lagrangian for a field of spin λ is equal to the cubic term in Yang–Mills theory, raised to the power λ. This result is valid for all λ for Lagrangians that contain a cubic interaction vertex involving three spin λ fields, in four-dimensional flat spacetime. For λ = 3, we present an additional derivation of this result.