Multispinor basis of fermi-bose transformations

Abstract

The multispinor description of particle fields and sources provides a unification of all spins and statistics. As such, it makes quite transparent the existence of transformations that alter the particle spin by 1 2 , with the accompanying F(ermi)-B(ose) transformation of statistics. After an initial discussion for noninteracting particles, both massive and massless, that is restricted to the exterior of sources (on-mass shell particles), the latter restriction is removed for special examples, including spinors of the second and third ranks. Some attention is given to the spinor description of the photon. The F-B spinor transformations are then presented in more familiar representations, for particular examples. The alternative constructions of integer spins using tensors and of integer +1 2 spins by means of tensor-spinors suggest transformations that change the spin by unity and retain the statistics. This is illustrated with a number of examples, including the photon and graviton. There is some additional discussion of the vector-spinor representation of spin 3 2 , including the massless limit and its transformations with the graviton. The starting point in this development is the existence of easily recognizable invariance or partial invariance transformations. Such transformations form a group, but the structure of that group has not been stated a priori. It is now investigated in various situations, among which are those for which the commutator transformation is a displacement, outside the sources. As is known from prior studies, the basic multiplets here are a pair of massless particles and a quartet of massive particles. For unit spin transformations, the multiplets are those of three-dimensional angular momentum for massless particles, and of four-dimensional angular momentum for massive particles. The latter is well known in the context of the degenerate hydrogen atom levels. A coda contains a brief discussion of interacting systems, using the example of spinor electrodynamics. It is found that exact invariance of the action can be achieved, with no mass restriction, by loosening the relations between field variations and source variations. These F-B transformations maintain their form under gauge transformations.