General trilinear interaction for arbitrary even higher spin gauge fields

TL;DR

This paper provides a comprehensive solution for constructing trilinear interactions among arbitrary higher spin gauge fields in flat spacetime, including classification and algebraic closure aspects.

Contribution

It introduces a complete method for arbitrary spin trilinear interactions and explores extensions to higher order interactions and gauge algebra closure.

Findings

Classification of cubic interactions based on derivatives and spin relations

Explicit construction of gauge transformations expanded in powers of the field

Discussion on potential extension to higher order interactions

Abstract

Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins $s_{1},s_{2}, s_{3}$ in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin $s$ gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.