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This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001.
Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective.
Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.
Gilles Halbout, Institut de Recherche Mathématique Avancée de Strasbourg, Strasbourg, France
Gilles Halbout: Deformation quantization, methods and applications to open problems · Giuseppe Dito and Daniel Sternheimer: Deformation quantization: genisis and metamorphoses · Giuseppe Dito: Asymptotic quantum electrodynamics · Boris Fedosov: On the trace density in deformation quantization · Daniel Arnaudon, Jean Avan, Luc Frappat and Eric Ragoucy: Deformed double Yangians and quasi-Hopf algebras · Stefan Waldmann: On the representation theory of deformation quantization · Claude Roger: Unimodular fields and deformation quantization · Christian Frønsdal: Harrison cohomology and abelian deformation quantization on algebraic varieties · Louis Boutet de Monvel: Related semi-classical and Toeplitz algebras · Alberto S. Cattaneo, Giovani Felder and Adriano Tomassini: Fedosov connections on jet bundles and deformation quantization · Dimitry Tamarkin: Deformation theory of Hopf algebras