Inconsistencies of Glass's equation for spin 3/2 particles

Abstract

A systematic study is made of the Glass equation for spin-3/2 particles with minimal electromagnetic interaction. The study is motivated by the knowledge that this equation is just as satisfactory as the Rarita-Schwinger equation in the absence of interactions and that a variety of problems crop up in the Rarita-Schwinger theory when minimal electromagnetic interaction is introduced. The hope that the Glass equation might fare better is belied, however, Not only does it suffer from the various ills (e.g., noncausal propagation, modes of complex frequency) which beset the Rarita-Schwinger theory but it also exhibits further troubles such as an increase in the number of "spin" degrees of freedom (something not encountered earlier in any theory with s<2), nonlocality of anticommutators of field components, etc., depending on the nature of the external field. Further, unlike in the symmetric tensor theory for spin 2, nonminimal interactions do not help to remove the anomaly of the abnormal number of degrees of freedom resulting from the minimal electromagnetic interaction. The bearing of the alebra of the β matrices on the difficulties of the interacting theories is briefly referred to.