Related papers: Quantum Clifford Algebras
We show that the binary representation of the integers has a role to play in many aspects of Clifford algebras.
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De…
We consider the Clifford algebra and the Clifford group associated with any quadratic module, degenerate or not, over an arbitrary commutative ring with 1. We determine some of the important subalgebras of the Clifford algebra under some…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed $gl(n)$ and $igl(n)$ algebras by a quantum fermionic space. We investigate a map between…
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
We derive a quantum deformation of the $W_N$ algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.
We establish for smooth projective real curves the equivalent of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
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…
Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.