Massive Higher Spin Fields Coupled to a Scalar: Aspects of Interaction and Causality

TL;DR

This paper analyzes the interactions of massive higher spin fields with a scalar, revealing that gauge invariance alone does not ensure correct degrees of freedom or causality, necessitating additional constraints for consistency.

Contribution

It provides a detailed examination of cubic interactions involving massive higher spin fields and scalar, highlighting the need for extra conditions beyond gauge invariance to ensure physical consistency.

Findings

Gauge invariance alone does not guarantee correct degrees of freedom.

Additional parameter constraints are necessary for massive higher spin fields.

Causality considerations impose further restrictions on interactions.

Abstract

We consider in detail the most general cubic Lagrangian which describes an interaction between two identical higher spin fieldsin a triplet formulation with a scalar field, all fields having the same values of the mass. After performing the gauge fixing procedure we find that for the case of massive fields the gauge invariance does not guarantee the preservation of the correct number of propagating physical degrees of freedom. In order to get the correct number of degrees of freedom for the massive higher spin field one should impose some additional conditions on parameters of the vertex. Further independent constraints are provided by the causality analysis, indicating that the requirement of causality should be imposed in addition to the requirement of gauge invariance in order to have a consistent propagation of massive higher spin fields.