Causality and indefiniteness of charge in spin 3/2 field theories

Abstract

The possibility of retaining causality of propagation of classical spin 3/2 fields in the presence of an external electromagnetic interaction is investigated. It is shown that in the case of the mixed spin 3/2-spin ½ theory of Bhabha and Gupta, causality in the interacting situation may be retained by giving up the positive definiteness of the free total charge and making an appropriate choice of the arbitrary parameters appearing in the Bhabha-Gupta Lagrangian. The authors demonstrate that the causal spin 3/2 equation proposed recently by Fisk and Tait (see abstr. A22979 of 1973) also shares the same feature, namely the indefiniteness of the free total charge.