Quantization of Relativistic Schrödinger Equations for Arbitrary Spin

Abstract

It is shown that a recently derived relativistic Schrödinger equation for free particles of arbitrary spin can be consistently quantized in the case of half-integer spins (but not for integer spins) by invoking the microcausality condition and using the role of certain expectation values of the $c$-number theory as generators of transformations of the Poincaré group in the $q$-number theory. The correct type of statistics (Fermi-Dirac) for half-integer-spin particles is obtained as a consequence of the theory. The way to handle the integer-spin case is indicated, but details are left for future presentation.