Schizosymmetry - A new paradigm for superfield expansions

A new principle of ‘schizosymmetry’ is proposed for interpreting superfield expansions over Grassmann parameters in quantum field theory. Symmetry generators Tphys, determining component field transformation properties, are allowed to depend on the grading via Tphys=Tℙe+T′ℙo, where ℙe and ℙo are the projections onto even and odd components in the Grassmann coordinates, respectively, and T and T′ correspond to different representations. Examples are given for both internal and space-time schizosymmetry. In the latter case, superfield expansions have components with both integer and half-integer spin. A program for the Lagrangian realization of schizosymmetry, including unified model building, is outlined.