BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields

Using BRST-BV formulation of relativistic dynamics, we study arbitrary spin massive and massless fields propagating in flat space. Generating functions of gauge invariant off-shell cubic interaction vertices for mixed-symmetry and totally symmetric fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives which provide a classification of cubic interaction vertices for such fields. As by product, we present simple expressions for the Yang–Mills and gravitational interactions of massive totally symmetric arbitrary spin fields.