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We consider in detail the most general cubic Lagrangian which describes aninteraction between two identical higher spin fieldsin a triplet formulationwith a scalar field, all fields having the same values of the mass. Afterperforming the gauge fixing procedure we find that for the case of massivefields the gauge invariance does not guarantee the preservation of the correctnumber of propagating physical degrees of freedom. In order to get the correctnumber of degrees of freedom for the massive higher spin field one shouldimpose some additional conditions on parameters of the vertex. Furtherindependent constraints are provided by the causality analysis, indicating thatthe requirement of causality should be imposed in addition to the requirementof gauge invariance in order to have a consistent propagation of massive higherspin fields.

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