Causality of propagation of spin-$\frac{3}{2}$ fields coupled to spinor and scalar fields

Recent investigations on the causality of propagation of spin-$\frac{3}{2}$ fields have revealed that the Bhabha-Gupta equation shares with the Fisk-Tait equation the advantage of being free from noncausality in the presence of minimal electromagnetic interaction, provided that the arbitrary parameters occurring in the theory are suitably restricted. Since the familiar Rarita-Schwinger theory is known to suffer from noncausality troubles the above-mentioned result is of considerable importance. We extend it in this paper by showing that causality is preserved in the above theories even in the presence of a different type of interaction involving scalar and spinor fields. Thus the result obtained earlier with the electromagnetic interaction is not merely a fortuitous circumstance.