Cubic interaction vertex of higher-spin fields with external electromagnetic field

TL;DR

This paper derives the cubic interaction vertex for charged bosonic higher-spin fields with a constant electromagnetic background, ensuring gauge invariance and causality in the first order of field strength.

Contribution

It provides the first explicit construction of the interaction vertex for arbitrary massive and massless bosonic higher-spin fields with external electromagnetic fields.

Findings

Complete interacting Lagrangian obtained for higher-spin fields

Gauge invariance maintained at first order in electromagnetic strength

Causality of massive spin-2 and spin-3 fields confirmed

Abstract

We fulfill the detailed analysis of coupling the charged bosonic higher spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic higher spin fields with external field is found. Construction is based on deformation of free Lagrangian and free gauge transformations by terms linear in electromagnetic field strength. In massive case a formulation with Stueckelberg fields is used. We begin with most general form of deformations for Lagrangian and gauge transformations, admissible by Lorentz covariance and gauge invariance and containing some number of arbitrary coefficients, and require the gauge invariance of the deformed theory in first order in strength. It yields the equations for the coefficients which are exactly solved. As a result, the complete interacting Lagrangian of arbitrary bosonic higher spin fields with constant electromagnetic field in first order in electromagnetic strength is obtained. Causality of massive spin-2 and spin-3 fields propagation in the corresponding electromagnetic background is proved.