Related papers: Hermite and Gegenbauer polynomials in superspace u…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
After a short introduction on Clifford algebras of polynomials, we give a general method of constructing a matrix representation. This process of linearization leads naturally to two fundamental structures: the generalized Clifford algebra…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold ($C$-space) consists not…
In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal…
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators…
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper,…
In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…
All 7-dimensional subalgebras of the 8-dimensional Clifford algebra over the field C of complex numbers are found. Canonical bases are used throughout the determination. It is found that the 8-dimensional Clifford algebra over C has exactly…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford…
A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…
Given two parallelisms of a projective space we describe a construction, called blending, that yields a (possibly new) parallelism of this space. For a projective double space $(\mathbb{P},\parallel_\ell,\parallel_r)$ over a quaternion skew…
We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the…
We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic…
We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested for high degrees. We conjecture a simple…
The Clifford action on superspaces is analyzed with a view on generalized Dirac fields taking values in some Clifford supermodule. the stress is here on two principles: complexification and polarisation. For applications in field theory,…
Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…
In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially…
A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in C^n is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an…