Superspinors and Graded Lorentz Groups in Three,Four and Five Dimensions

Three superalgebras osp(1; 2; F) (F = R, C, H) and corresponding three supergroups are considered. The transformation laws of spinors with anticommuting components for 3-dimensional (O(2, 1) ≃ Sp(2; R)), 4-dimensional (O(3, 1) ≃ Sp(2, C)) and 5-dimensional (O(4, 1) ≃ Sp(2; H)) Lorentz group are extended in a supersymmetric way by introducing nonlinear realizations of the supergroups OSp(1, 2; F). The affine Grassmann spinors in all three cases are obtained by suitable “flat” limit of the nonlinear realization. Different gradings and different contractions of osp(1,2; F) (F = R, C, H) superalgebras are considered.