Toward a theory of particles with 3/2 spin

A detailed analysis is performed of the pattern of meshes of irreducible Lorentz group representations corresponding to the direct product of vector and bispinor representations within the framework of the Gel'fand-Yaglom approach, for the purpose of determining the possibility of constructing various relativistic wave equations describing particles with a maximum spin of 3/2. Two such new equations are constructed for a 3/2 spin, which differ from the generally known Rarita-Schwinger and Fierz-Pauli equations. The nonequivalence of the latter is also proven.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–95, January, 1985.