Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole - Université Polytechnique des Hauts-de-France Accéder directement au contenu
Article Dans Une Revue Journal of Geometry and Physics Année : 2016

Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole

Résumé

In our previous publications we introduced differential calculus on the enveloping algebras U (gl(m)) similar to the usual calculus on the commutative algebra Sym(gl(m)). The main ingredients of our calculus are quantum partial derivatives which turn into the usual partial derivatives in the classical limit. In the particular case m = 2 we prolonged this calculus on a central extension A of the algebra U (gl(2)). In the present paper we consider the problem of a further extension of the quantum partial derivatives on the skew-field of the algebra A and define the corresponding de Rham complex. As an application of the differential calculus we suggest a method of transferring dynamical models defined on an extended Sym(u(2)) to an extended algebra U(u(2)). We call this procedure the quantization with noncommutative configuration space. In this sense we quantize the Dirac monopole and find a solution of this model.
Fichier principal
Vignette du fichier
1512.03495.pdf (194.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03172942 , version 1 (05-07-2022)

Identifiants

Citer

Dimitri Gurevich, Pavel Saponov. Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole. Journal of Geometry and Physics, 2016, 106, pp.87-97. ⟨10.1016/j.geomphys.2016.03.007⟩. ⟨hal-03172942⟩
22 Consultations
11 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More