Spin 3 cubic vertices in a frame-like formalism

TL;DR

This paper demonstrates that using a frame-like formalism simplifies the construction of interaction vertices for massless spin 3 fields, providing explicit Lagrangians and gauge transformations, and confirming gauge algebra closure.

Contribution

It introduces a frame-like formalism approach to derive interaction vertices for massless spin 3 fields, simplifying previous metric-like methods and explicitly constructing gauge-invariant Lagrangians.

Findings

Explicit vertices for spin 3 interactions with lower spins

Gauge transformations and algebra closure verified

Simplification over metric-like formalism

Abstract

Till now most of the results on interaction vertices for massless higher spin fields were obtained in a metric-like formalism using completely symmetric (spin-)tensors. In this, the Lagrangians turn out to be very complicated and the main reason is that the higher the spin one want to consider the more derivatives one has to introduce. In this paper we show that such investigations can be greatly simplified if one works in a frame-like formalism. As an illustration we consider massless spin 3 particle and reconstruct a number of vertices describing its interactions with lower spin 2, 1 and 0 ones. In all cases considered we give explicit expressions for the Lagrangians and gauge transformations and check that the algebra of gauge transformations is indeed closed.