Deformation quantization for Heisenberg supergroup
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Deformation quantization for Heisenberg supergroup
Author(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]
Journal title :
Journal of Functional Analysis
Pages :
549-603
Publisher :
Elsevier
Publication date :
2012-05-12
ISSN :
0022-1236
English keyword(s) :
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
HAL domain(s) :
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]
English abstract : [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: ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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