Skew-symmetric tensor-spinor formulation of the spin 3/2 field

Abstract

The formulation of a field theory for a spin ³/₂ particle is sought in terms of a skew-symmetric tensor-spinor. If the wavefunction transforms irreducibly under the rotation group, the lagrangian density is not hermitian, but if it transforms as the direct sum of two spin ³/₂ components, this defect is removed. Furthermore, when minimal coupling to the electromagnetic field is introduced in the latter case, propagation remains causal, so that some improvement over the usual vector-spinor theory is achieved.