POLYVECTOR SUPER-POINCARÉ ALGEBRAS, M, F THEORY ALGEBRAS AND GENERALIZED SUPERSYMMETRY IN CLIFFORD-SPACES

Abstract

Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic supersymmetric point-particle action in Clifford-space backgrounds. The relativistic supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector super-Poincaré and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-superspace realizations of generalized supersymmetries in Clifford spaces.