The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups the form 36:L4(3). These groups are all isomorphic to each other and order 4421589120 with index 1120 in (3). In this paper, we will compute ordinary carácter table one these using technique Fischer-Clifford matrices. This is very efficient character an extension Ḡ = N.G especially where normal subgroup N element...

The functional quantum field theory, developed by Stumpf, provides the possibility to derive the quantum dynamics of a positronium gas from Coulomb interacting electrons and positrons. By this example, the method will be brought in a Clifford algebraic light, through identifying the functional space with an infinite dimensional Euclidean Clifford algebra.

Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K -theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as more geometric topics of invariant theory, e.g., the Graßmann-Cayley bracket algebra are all covered by the Hopf algebraic framework. The new branch of experim...

A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: “extra dimensions” are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1)×SU(2)×SU(3) gauge group....

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...