On a class of relativistic wave-equations of spin 3/2

Abstract

The entire class of relativistic wave equations derivable from the Lagrange function ψ °D(α^k pk +ßΧ)ψ and in which the wave function transforms according to the representation R (3/2, ½)+R(½, ½) of the Lorentz group is studied. It is shown that there is only one equation in this class describing particles of finite mass in which the charge density is positive definite, namely, the equation equivalent to the set proposed by Dirac, Fierz and Pauli for a particle of spin 3/2. It is shown that there is no equation in this class which describes a particle of spin 3/2 and zero rest mass. There is an equation in this class in which the particle has a state of finite rest mass and spin 3/2 and another state of zero mass and spin ½. In the former state the free charge density is positive definite in the latter zero.