Spinor Currents as Vector Particles

We study a prototype for the problem of determining the irreducible factors of the spaces spanned by currents between homogeneous vector bundles. More specifically, letGdenote the conformal group of Minkowski space–timeM0, or more precisely,SU(2, 2). It is shown that the positive-energy unitaryG-irreducible massive factors of the one-form bundle over the conformal compactification ofM0are bundle-equivalent to spaces spanned by currents of the spinor bundle. This has the interpretation that theZ-particle may be modelled by the representation ofGof lowestK-type (“LKT”) (3,emsp14;1/2, 1/2), whereK=SU(1)×SU(2)×SU(2) and (m, j, j′) refers to the representation in which the lowest eigenvalue of theSU(1) generator ism, whilejandj′ are the spins of the left and rightSU(2) representations. In particular, this “Z” representation is bundle-equivalent to the representation ofGin a space of currents between neutrinos, of LKT (3/2, 0, 1/2), and antineutrinos, of LKT (3/2, 1/2, 0). TheW±-particle representation may similarly be modelled by the representation ofGof lowestK-type (4, 0, 0), the only other massive positive-energy unitary factor of the one-form bundle. In particular, theW−is equivalent to a space of currents between the electron, of LKT (5/2, 0, 1/2), and the antineutrino. These results are consistent with the possibility that all quasi-stable elementary particles may be modelled by similar subspaces of bundle products.