Pierre Bieliavsky
Université catholique de Louvain
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Featured researches published by Pierre Bieliavsky.
Memoirs of the American Mathematical Society | 2015
Pierre Bieliavsky; Victor Gayral
Introduction Notations and conventions Oscillatory integrals Tempered pairs for Kahlerian Lie groups Non-formal star-products Deformation of Frechet algebras Quantization of polarized symplectic symmetric spaces Quantization of Kahlerian Lie groups Deformation of
Letters in Mathematical Physics | 2001
Pierre Bieliavsky; Marc Massar
C^*
Journal of Functional Analysis | 2012
Pierre Bieliavsky; Axel Marcillaud de Goursac; Gijs M. Tuynman
-algebras Bibliography
Communications in Mathematical Physics | 2009
Pierre Bieliavsky; Stéphane Detournay; Philippe Spindel
We use star representation geometric methods to obtain explicit oscillatory integral formulae for strongly invariant star products on Iwasawa subgroups AN of SU(1,n)
Journal of High Energy Physics | 2004
Pierre Bieliavsky; Stéphane Detournay; Philippe Spindel; Marianne Rooman
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 noncom- mutative quantum field theory.
Nuclear Physics | 2002
Pierre Bieliavsky; Marianne Rooman; Philippe Spindel
We describe the space of (all) invariant, both formal and non-formal, deformation quantizations on the hyperbolic plane
Physics Letters B | 2003
Pierre Bieliavsky; Stéphane Detournay; Michel Herquet; Marianne Rooman; Philippe Spindel
Math.Phys.Stud. | 1995
Pierre Bieliavsky; Michel Cahen; Simone Gutt
{\mathbb D}
Reviews in Mathematical Physics | 2003
Pierre Bieliavsky; Simone Gutt; Martin Bordemann; Stefan Waldmann
Geometriae Dedicata | 1998
Pierre Bieliavsky
as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a unified method producing every quantization of