Cubic interaction vertices in higher spin theories

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