Consistency Condition for Propagators

It is shown that there is a strict condition for the propagators of higher-spin particles. We require the consistency of the propagator when a particle propagates by means of self-energy-type interactions. We require a kind of unitarity. Then this requirement turns out to be a strict condition in the case of higher-spin particles. Its nontriviality is due to the fact that free fields of higher-spin particles contain redundant components, which are suppressed by means of subsidiary conditions, not satisfied by the currents coupled with the fields. The usual propagators do not satisfy our requirement, while those which have been introduced in connection with the $O\left(4\right)\mathrm{}$ symmetry satisfy it. Also, a difficulty of the scalar-tensor theory of the graviton is pointed out. DOI: http://dx.doi.org/10.1103/PhysRevD.2.2255 © 1970 The American Physical Society