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Deformation on phase space.

Oscar Arratia, M.ª Angeles Martín Mínguez, María Angeles del Olmo (2002)

RACSAM

El trabajo que presentamos constituye una revisión de varios procedimientos de cuantización basados en un espacio de fases clásico M. Estos métodos consideran a la mecánica cuántica como una "deformación" de la mecánica clásica por medio de la "transformación" del álgebra conmutativa C∞(M) en una nueva álgebra no conmutativa C∞(M)ħ. Todas estas ideas conducen de modo natural a los grupos cuánticos como deformación (o cuantización en un sentido amplio) de los grupos de Poisson-Lie, lo cual también...

Deformed Heisenberg algebra with reflection and d -orthogonal polynomials

Fethi Bouzeffour, Hanen Ben Mansour, Ali Zaghouani (2017)

Czechoslovak Mathematical Journal

This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d -orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1 . The underlying algebraic framework allowed a systematic derivation...

Designs, groups and lattices

Christine Bachoc (2005)

Journal de Théorie des Nombres de Bordeaux

The notion of designs in Grassmannian spaces was introduced by the author and R. Coulangeon, G. Nebe, in [3]. After having recalled some basic properties of these objects and the connections with the theory of lattices, we prove that the sequence of Barnes-Wall lattices hold 6 -Grassmannian designs. We also discuss the connections between the notion of Grassmannian design and the notion of design associated with the symmetric space of the totally isotropic subspaces in a binary quadratic space, which...

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