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. It is shown that the covariant Dirac equation in C-space contains Yang-Mills fields of the U(1)× SU(2)×SU(3) group as parts of the generalized spin connection of the C-space.

CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in C (B) the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for the Clifford product are implemented: cmulNUM based on Chevalley’s recursive formula, and cmulRS based on a non-recursive Rot...

CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for Clifford product are implemented: cmulNUM based on Chevalley’s recursive formula, and cmulRS based on non-recursive Rota-Stei...

In this paper using the Clifford bundle formalism a Lagrangian theory of the Yang-Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski spacetime is presented. It is shown how two simple hypothesis permits the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry int...

In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of R3. We express the admissibility condition in terms of a Cl3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how...

We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. This work was partially supported by CONACYT Project 1821-E9211, Mexico. On leave from the Odessa State University.

We define a normal form for Clifford circuits, and we prove that every Clifford operator has a unique normal form. Moreover, we present a rewrite system by which any Clifford circuit can be reduced to normal form. This yields a presentation of Clifford operators in terms of generators and relations.

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into ...

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with StueckelbergSchrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five dimensional theory prevents a natural generalization of the Dirac monopole, since the theory is not symme...