Lanczos's equation as a way out of the spin 3/2 crisis?

Abstract

It is shown (1) that Lanczos's quaternionic formulation of Dirac's equation does not lead to a solution of the problems that plague the standard spin 3/2 theory based on the Rarita-Schwinger equation, but (2) that the four-component solutions to the quaternionic generalization of Dirac's equation proposed by Lanczos in 1929 may provide a consistent theory for spin 3/2 particles, although at the cost of giving up the postulate that there should be a one-to-one correspondence between arbitrary-high-spin unitary representations of the inhomogeneous Lorentz group and elementary particles.