Towards the structure of a cubic interaction vertex for massless integer higher spin fields

TL;DR

This paper clarifies the structure of cubic interaction vertices for massless higher spin fields in Minkowski space, providing explicit operator forms using the BRST approach to handle irreducibility constraints.

Contribution

It introduces an explicit form of the operator Z_j for cubic vertices of massless higher spin fields, advancing the understanding of their interaction structure.

Findings

Explicit form of the operator Z_j for cubic vertices

Solution within the BRST framework including all constraints

Clarification of the vertex structure for irreducible higher spin fields

Abstract

The structure of a cubic Lagrangian vertex is clarified for irreducible fields of helicities $s_1, s_2, s_3$ in a $d$-dimensional Minkowski space. An explicit form of the operator $\mathcal{Z}_j$ entering the vertex in a non-multiplicative way (examined in arXiv:2105.12030[hep-th] for $j=1$) is obtained. The solution is found within the BRST approach with complete BRST operators, which contain all constraints corresponding to the conditions that extract the irreducible fields, including trace operators.