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

TL;DR

This paper explores superfield expansions with vector Grassmann variables, introduces schizofields containing mixed spins, and demonstrates an $sl(2/1,{ m C})_{ m R}$ supersymmetry at the component level, with potential applications to particle spectra.

Contribution

It establishes a new classification of schizofields with mixed spins and demonstrates supersymmetry in these fields, advancing superfield theory with vector Grassmann variables.

Findings

Identification of schizofields with integer and half-integer spins.

Demonstration of $sl(2/1,{ m C})_{ m R}$ supersymmetry in certain schizofields.

Prospects for schizofield calculus and particle spectrum applications.

Abstract

Superfield expansions over four-dimensional graded spacetime $(x^\mu,\theta^\nu)$, with Minkowski coordinates $x$ extended by vector Grassmann variables $\theta$, 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.