Here is discussed generalization of Clifford algebras, l-dimensional Weyl–Clifford algebras T(n, l) with n generators tk satisfying equation ∑n k=1 aktk )l = ∑n k=1 (ak) . It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such ...

The Clifford tori in S constitue a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one ...

Abstract. In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of t...

It is shown how a Conformal Gravity and U(4)×U(4) Yang-Mills Grand Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4, C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity and t...

Recently author suggested [23] an application of Clifford algebras for construction of a " compiler " for universal binary quantum computer together with later development [24] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. ...

We formulate a real quantum theory with an orthogonal group, broken by an approximate i operator, supposed to underlie the present complex quantum theory, with its unitary group. A real quantum theory requires a real quantum statistics. We put forward a general concept of linear statistics that embraces the usual complex tensorial statistics (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein), t...

One of the main goals of these notes is to explain how rotations in R are induced by the action of a certain group Spin(n) on R, in a way that generalizes the action of the unit complex numbers U(1) on R, and the action of the unit quaternions SU(2) on R (i.e., the action is defined in terms of multiplication in a larger algebra containing both the group Spin(n) and R). The group Spin(n), calle...

In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again for a fixed vector in the image space, ...

A great reformer has passed on. Clifford Whittingham Beers died on July 9th, 1943, at Providence, U.S.A., but his fine enthusiastic and farseeing spirit has left behind it work which persists and grows. At a time when such ideas as his were regarded as almost too progressive, and, in some quarters indeed, as subversive and revolutionary, he, a recovered patient, demonstrated the value of indivi...

We generalize Beurling's theorem for the Clifford-Fourier transform and give some of its applications. deduce analogs Hardy, Cowling-Price, Gelfand-Shilov theorems in Clifford analysis setting.