On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation

TL;DR

This paper constructs a local quartic interaction between higher-spin gauge fields and scalars, analyzing gauge symmetry closure and transformation algebra in the linear approximation.

Contribution

It presents a novel construction of the interacting Lagrangian for higher-spin fields with scalars using Noether's procedure, including gauge transformation and commutator analysis.

Findings

Derived linear gauge transformations for higher-spin fields.

Analyzed the gauge transformation algebra and its closure.

Classified the commutator's right-hand side in terms of cubic interactions.

Abstract

Local quartic interaction of higher-spin gauge field with a scalar field is considered. In this special case, the nontrivial task of construction of interacting Lagrangian for the higher spin field in physical gauge was solved using the full power of Noether's procedure. As a result, the linear on-field gauge transformation is obtained and the corresponding commutator of transformation is analyzed. To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric tensor fields and with mixed symmetry tensor fields transformations.