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

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 sl(2/1, ℂ)ℝ 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.