Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

Abstract

We construct the Rarita–Schwinger basis vectors, [Formula: see text], spanning the direct product space, [Formula: see text], of a massless four-vector, [Formula: see text], with massless Majorana spinors, [Formula: see text], together with the associated field-strength tensor, [Formula: see text]. The [Formula: see text] space is reducible and contains one massless subspace of a pure spin-[Formula: see text]. We show how to single out the latter in a unique way by acting on [Formula: see text] with an earlier derived momentum independent projector, [Formula: see text], properly constructed from one of the Casimir operators of the algebra [Formula: see text] of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless [Formula: see text] carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as [Formula: see text]. The conclusion is that the [Formula: see text] bi-vector spinor field can play the same role with respect to a [Formula: see text] gauge field as the bi-vector, [Formula: see text], associated with the electromagnetic field-strength tensor, [Formula: see text], plays for the Maxwell gauge field, [Formula: see text]. Correspondingly, we find the free electromagnetic field equation, [Formula: see text], is paralleled by the free massless Rarita–Schwinger field equation, [Formula: see text], supplemented by the additional condition, [Formula: see text], a constraint that invokes the Majorana sector.