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]

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

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]

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 >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL