Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

TL;DR

This paper constructs a gauge-invariant quartic interaction vertex for massive higher spin fields coupled to a constant electromagnetic field using a BRST approach, without imposing off-shell constraints.

Contribution

It introduces a novel unconstrained BRST-based method to derive quartic interaction vertices for higher spin fields in external electromagnetic backgrounds.

Findings

Derived explicit form of the quartic interaction vertex

Maintained gauge invariance without off-shell constraints

Applicable to arbitrary spacetime dimensions

Abstract

We consider the massive integer higher spin fields coupled to an external constant electromagnetic field in flat space of arbitrary dimension and find a gauge invariant quartic interaction vertex which is quadratic in dynamical higher spin field and quadratic in external field. Construction of the vertex is based on the BRST approach to higher spin filed theory where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning (unconstrained formulation).