Related papers: Clifford semialgebras
We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored…
In this paper we combine methods from projective geometry, Klein's model, and Clifford algebra. We develop a Clifford algebra whose Pin group is a double cover of the group of regular projective transformations. The Clifford algebra we use…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous papers. On the basis of new classification of Clifford algebra elements it is possible to find out…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…
A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.
We construct new relativistic linear differential equation in $d$ dimensions generalizing Dirac equation by employing the Clifford algebra of the cubic polynomial associated to Klein-Gordon operator multiplied by the mass parameter. Unlike…
We study the representation theory and enveloping $C^*$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^*$-algebras under consideration as algebras of continuous matrix-functions satisfying certain…
We introduce a notion of matrix valued Gram decompositions for correlation matrices whose study is motivated by quantum information theory. We show that for extremal correlations, the matrices in such a factorization generate a Clifford…
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra…
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this…
We present some results about the irreducible representations appearing in the exterior algebra $\Lambda \mathfrak{g}$, where $ \mathfrak{g}$ is a simple Lie algebra over $\mathbb{C}$. For Lie algebras of type $B$, $C$ or $D$ we prove that…
The physical fields (electromagnetic and electron fields) considered in the framework of Clifford algebras $\C_2$ and $\C_4$. The electron field described by the algebra $\C_4$ which in spinor representation is realized by well-known Dirac…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials,…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
We give a one dimensional octonionic representation of the different Clifford algebra $Cliff(5,5)\sim Cliff(1,9), Cliff(6,6)\sim Cliff(2,10)$ and lastly $Cliff(7,6)\sim Cliff(3,10)$.