Deformation quantization for Heisenberg supergroup
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Deformation quantization for Heisenberg supergroup
Auteur(s) :
Bieliavsky, Pierre [Auteur]
Institut de Recherche en Mathématiques et Physique [UCL IRMP]
de Goursac, Axel [Auteur correspondant]
Institut de Recherche en Mathématiques et Physique [UCL IRMP]
Tuynman, Gijs M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut de Recherche en Mathématiques et Physique [UCL IRMP]
de Goursac, Axel [Auteur correspondant]
Institut de Recherche en Mathématiques et Physique [UCL IRMP]
Tuynman, Gijs M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Titre de la revue :
Journal of Functional Analysis
Pagination :
549-603
Éditeur :
Elsevier
Date de publication :
2012-05-12
ISSN :
0022-1236
Mot(s)-clé(s) en anglais :
Deformation quantization
Heisenberg supergroup
Harmonic analysis
Fréchet functional spaces
Graded operator algebras
Supermanifolds
Renormalization
Heisenberg supergroup
Harmonic analysis
Fréchet functional spaces
Graded operator algebras
Supermanifolds
Renormalization
Discipline(s) HAL :
Mathématiques [math]/Algèbres quantiques [math.QA]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Résumé en anglais : [en]
We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d . However, the method used here differs from Rieffel's one: ...
Lire la suite >We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d . However, the method used here differs from Rieffel's one: we obtain a Universal Deformation Formula for the actions of R^{m|n} as a byproduct of Weyl ordered Kirillov's orbit method adapted to the graded setting. To do so, we have to introduce the notion of C* -superalgebra, which is compatible with the deformation, and which can be seen as corresponding to noncommutative superspaces. We also use this construction to interpret the renormalizability of a noncommutative quantum field theory.Lire moins >
Lire la suite >We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d . However, the method used here differs from Rieffel's one: we obtain a Universal Deformation Formula for the actions of R^{m|n} as a byproduct of Weyl ordered Kirillov's orbit method adapted to the graded setting. To do so, we have to introduce the notion of C* -superalgebra, which is compatible with the deformation, and which can be seen as corresponding to noncommutative superspaces. We also use this construction to interpret the renormalizability of a noncommutative quantum field theory.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
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