A note on irreducibility and existence of integer spin zero-rest-mass fields

It is shown that only for spins 1 and 2 (electronmagnetism and gravitation) does the generic integer spin, source-free, zero-rest-mass field generate an irreducible representation of the proper orthochronous Lorentz group,L+. The conclusion is then drawn that as these higher-spin fields can in no sense be considered as elementary we have strong mathematical (and physical) grounds for their (apparent) nonexistence in nature.