The main objective of this paper is to clarify the ontology of DiracHestenes spinor fields (DHSF ) and its relationship with sum of even multivector fields, on a general Riemann-Cartan spacetime M=(M, g,∇, τg, ↑) admitting a spin structure and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE ) when M is a Lorentzian spacetime. To this aim we introduce t...

We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a reversible quantum logic for the Quantum Universe As Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality. It has a Clifford algebra of “cosmonions,” extending the quaternions to a cosmological number of anticommuting units. Its qubits obey Clifford-Wilczek statistics and ...

A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple system in terms of 8-component spinors associated with the Clifford algebras C(0, 7) and C(4, 3).

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4, 0), this parametrizat...