On the admissible Lorentz group representations in unique-mass, unique-spin relativistic wave equations

Abstract

Considering the infinite class of relativistic wave equations wherein the transformation property of the wavefunction involves up to four (unspecified) inequivalent irreducible representations (IIRs) of the Lorentz group occurring with arbitrary multiplicities, the authors have investigated the general question as to what combinations of IIRs would be admissible and with what multiplicities, if it were required that the cautions have solutions only for a single (unspecified) spin and mass and be inequivalent to any simpler equation. It is found that the possibilities are quite limited. The main results are presented.