On schizosymmetric superfields and sl(2/1,C)_R supersymmetry

Abstract

Superfield expansions over four-dimensional graded spacetime $(x^μ,θ^ν)$, 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 $sl(2/1,{\mathbb C})_{\mathbb R}$ supersymmetry at the component field level is demonstrated. Prospects for a schizofield calculus, and application of these types of fields to the particle spectrum, are adumbrated.