New Inconsistencies in the Quantization of Spin-32Fields

Abstract

The possibility of consistently quantizing a spin-$\frac{3}{2}$ field in the presence of a coupling to a scalar and a spinor field is considered. It is found that, contrary to a recent assertion, the anticommutators of the various Fermi-Dirac fields are not positive definite. Inasmuch as this inconsistency is found to be present for the case in which the $\frac{3}{2}$ field participates only linearly in the interaction, such a result demonstrates that the difficulties discovered by Johnson and Sudarshan for an electromagnetic coupling can be expected to occur for a considerably more general class of interactions.