On schizosymmetric superfields and $sl(2/1, \Bbb{ C})_\Bbb{R}$ supersymmetry

Abstract

Superfield expansions over four-dimensional graded spacetime (xµ,θν), with Minkowski coordinates x extended by vector Grassmann variables θ, are investigated. By appropriate identification of the physical Lorentz algebra in the even and odd parts of the superfield, a typology of `schizofields' containing both integer and half-integer spin fields is established. For two of these types, identified as `gauge potential'-like and `field strength'-like schizofields, an supersymmetry at the component field level is demonstrated. Prospects for a schizofield calculus, and application of these types of field to the particle spectrum, are adumbrated.