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Analyse et modèles dynamiques non commutatifs sur l'espace de q-Minkowski

Abstract : The present thesis deals with the large field of noncommutative geometry. This field is extensively studied because of mathematicians and physicists' common opinion that noncommutative geometry methods are useful tools to describe dynamical processes at Planck length. So the main purpose of this thesis is to provide a generalization of some dynamical models defined on Minkowski space on its q-analog. Since the creation of the Quantum Group theory by Drinfeld, numerous attempts have been made to introduce dynamical models which are covariant under quantum groups. Most interesting are models built on the q-Minkowski space algebra. P. Kulish showed that this algebra is a particular case of the so-called modified Reflection Equation Algebra which is linked to an operator called Hecke symmetry. So we are defining here dynamical models which are deformations of their classical counterparts. Then we are looking for integrals of dynamics, which leads us to define analogs of energy and the Runge-Lenz vector. At the end of this work, we will generalize the partial differential equations of field theory and particularly Maxwell's operator.
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https://tel.archives-ouvertes.fr/tel-00289899
Contributor : Antoine Dutriaux <>
Submitted on : Monday, June 23, 2008 - 10:50:33 PM
Last modification on : Friday, November 13, 2020 - 8:44:12 AM
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Antoine Dutriaux. Analyse et modèles dynamiques non commutatifs sur l'espace de q-Minkowski. Mathématiques [math]. Université de Valenciennes et du Hainaut-Cambresis, 2008. Français. ⟨tel-00289899⟩

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