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.Comment: 34 pages, comments, references and one Appendix added. Typos
corrected. Published versio
