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

abstract

  • We construct the Rarita-Schwinger basis vectors, Uμ, spanning the direct product space, Uμ:= Aμ u M, of a massless four-vector, Aμ, with massless Majorana spinors, uM, together with the associated field-strength tensor, μν:= pμUν - pνUμ. The μν space is reducible and contains one massless subspace of a pure spin-3/2 (3/2, 0) (0, 3/2). We show how to single out the latter in a unique way by acting on μν with an earlier derived momentum independent projector, (3/2,0), properly constructed from one of the Casimir operators of the algebra so(1, 3) of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless (3/2, 0) (0, 3/2) carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as [w(3/2,0)]μν:= [(3/2,0)]μν γγ. The conclusion is that the (3/2, 0) (0, 3/2) bi-vector spinor field can play the same role with respect to a Uμ gauge field as the bi-vector, (1, 0) (0, 1), associated with the electromagnetic field-strength tensor, Fμν, plays for the Maxwell gauge field, Aμ. Correspondingly, we find the free electromagnetic field equation, pμF μν = 0, is paralleled by the free massless Rarita-Schwinger field equation, pμ[w(3/2,0)] μν = 0, supplemented by the additional condition, γμγν[w(3/2,0)] μν = 0, a constraint that invokes the Majorana sector. © 2019 World Scientific Publishing Company.

publication date

  • 2019-01-01