Spinor currents as vector particles (Q1270240)

This is a continuation of a previous paper by the first author [\textit{I. Segal}, J. Funct. Anal. 154, 542-558 (1998; Zbl 0912.53059), see the preceding review], in which a prototype for the problem of determining the irreducible factors of the spaces spanned by currents between homogeneous vector bundles are studied. When the conformal group \({\mathbf G}= SU(2,2)\) of a Minkowskian spacetime \({\mathbf M}\) is chosen, it is shown that the positive-energy unitary \({\mathbf G}\)-irreducible massive factors of the one-form bundle over the conformal compactification of \({\mathbf M}\) are bundle-equivalent to spaces spanned by currents of the spinor bundle. These notions are examined for the representations of the \(Z\), \(W^+\), and \(W^-\) particles, and are consistent with the possibility that all quasi-stable elementary particles may be modeled by suitable subspaces of bundle products. Contents include: an introduction; technical preliminaries; and spinor currents.