Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discre...

It is shown how one can attain the desired locally causal property of QM in Clifford-spaces despite the spacelike separation of two massive spin-12 particles involved in the Einstein-Podolksy-Rosen (EPR) experiment. This is achieved by proving why the addition laws of the particles poly-vector-valued momentum in Clifford-space is null-like. This is the key reason why it is possible to implement...

Appell systems can be interpreted as polynomial solutions of generalized heat equations, and in probability theory they have been used to obtain non-central limit theorems. The natural grade-decomposition of a Clifford algebra of arbitrary signature lends it a natural Appell system decomposition. Motivated by evolution equations on Clifford algebras, combinatorial raising and lowering operators...

A Moyal deformation of a Clifford Cl(3, 1) Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant Θ parameters). In the very special case when one imposes certain constraints on the fields, there are no first order contributions in the Θ parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does not impose constraints on...

We extend the construction of Born’s Reciprocal Phase Space Relativity to the case of Clifford Spaces which involve the use of polyvectors and a lower/upper length scale. We present the generalized polyvector-valued velocity and acceleration/force boosts in Clifford Phase Spaces and find an explicit Clifford algebraic realization of the velocity and acceleration/force boosts. Finally, we provid...

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called Ck hierarchy gates, intro...

Introductory and historical remarks Clifford (1878) introduced his ‘geometric algebras’ as a generalization of Grassmann algebras, complex numbers and quaternions. Lipschitz (1886) was the first to define groups constructed from ‘Clifford numbers’ and use them to represent rotations in a Euclidean space. É. Cartan discovered representations of the Lie algebras son(C) and son(R), n > 2, that do ...

It is a well known fact from the group theory that irreducible tensor representations of classical groups are suitably characterized by irreducible representations of the symmetric groups. However, due to their different nature, vector and spinor representations are only connected and not united in such description. Clifford algebras are an ideal tool with which to describe symmetries of multip...