Abstract
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.
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