On two relativistic equations for spin-3/2 tensor spinor fields

Abstract

We compare two equations for tensor spinor fields of spin 3/2: the Fisk-Tait equation and one which we have proposed recently. These are seen to have Harish-Chandra minimal equations of different degrees, thus illustrating a possibility studied by Glass previously. Their Γ-matrices are related in such a way that\((\Gamma .p)^3 - p^2 (\Gamma .p)\). The equations are shown to be equivalent in many interactions, including minimal electromagnetic coupling, although, as we argue, one of the two forms would be simpler to deal with. The structure of the equation is displayed through a change of basis and the Schrodinger equation form is obtained for the pure spin-3/2 component of the field.