Massive and massless supersymmetry: Multiplet structure and unitary irreducible representations

Abstract

UIR’s of the supersymmetry algebra for the massive and massless cases are analyzed covariantly (without the use of induced representations) in terms of their component spins. For the massive case normalized basis vectors ‖p2≳0, j0; σ; pjλ〉 are constructed, where j0 is the ’’superspin’’ and σ is an additional quantum number serving to distinguish the different ‖pjλ〉, the constituent p2≳0, spin-j UIR’s of the Poincaré group. For the massless case, normalized basis vectors ‖p2=0, λ0; pλ〉 are similarly constructed, where λ0 is the ’’superhelicity.’’ Matrix elements of the supersymmetry generators, in these bases, are explicitly given. The ’’σ basis’’ is used to define weight diagrams for the massive UIR’s of supersymmetry, and their properties are briefly described. Eigenfunctions ωσ(ϑ) are also defined, and their connection with the reduction of higher spin massive superfields ΦJ(x,ϑ) is discussed. Finally, it is shown how gauge dependence necessarily arises with certain massless superfields. The massless scalar superfield, both gauge-dependent and gauge-independent, is discussed as an example.