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

TL;DR

This paper develops a BRST-BV framework to systematically construct and classify cubic interaction vertices for both massive and massless higher-spin fields in flat space, including gauge-invariant and symmetry considerations.

Contribution

It introduces a method to generate gauge-invariant cubic vertices for mixed-symmetry and symmetric higher-spin fields, providing new classifications and explicit interaction expressions.

Findings

Derived restrictions on spins and derivatives for symmetric fields.

Provided explicit forms for Yang-Mills and gravitational interactions.

Classified cubic vertices for various higher-spin configurations.

Abstract

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.