A Clifford algebra has three major multiplications: inner product, outer product and geometric product. Accordingly, the same Clifford algebra has three versions: Clifford vector algebra, which features on inner products and outer products of multivectors; Clifford bracket algebra, which features on pseudoscalars and inner products of vectors; Clifford geometric algebra, which features on geome...

The Clifford spectrum is an elegant way to define the joint of several Hermitian operators. Examples as small a triple 2×2 matrices can have that two-dimensional manifold. To date, there are very few noncommuting examples where has been computed. Our main goal generation various three or four we calculate spectrum. In some cases, our results rigorous, perhaps involving assistance from computer ...

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 pointparticle action in Clifford-space backgrounds. The relativistic Supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the ...

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have focused on systems which the Hamiltonian consists matrices that commute with each other satisfy Clifford algebra. In this work, we consider Hamiltonians are beyond minimal model. Specifically, two types layered is studied, consisting do not...

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 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 paper gives a new representation of conformal groups in n dimensions terms hyperquaternions defined as tensor products quaternion algebras (or subalgebra thereof). Being Clifford algebras, provide good pseudo-orthogonal such $$O(p+1,q+1)$$ isomorphic to the nD group with $$n=p+q.$$ yields simple expressions generators, independently matrices or operators. canonical decomposition and invaria...

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven...

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in spin representation (a.k.a. rotors) terms their generators text]: This is general to geometric algebras real Clifford algebras) dimension text], naturally generalizing Rodrigues’ rotations text]. In particular, it applies rotors within framework Hestenes’ spacetime ...