Noncommutative Spacetimes Symmetries in Noncommutative Geometry and

There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based o

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Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at springerlink.com. The series content is indexed, abstracted and referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer: Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg / Germany [email protected]

P. Aschieri M. Dimitrijevi´c P. Kulish F. Lizzi J. Wess

Noncommutative Spacetimes Symmetries in Noncommutative Geometry and Field Theory

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Paolo Aschieri Centro “E. Fermi”, Roma, and U. Piemonte Orientale, Alessandria and INFN Sezione di Torino Gruppo Collegato di Alessandria Via Teresa Michel 11 15100 Alessandria Italy [email protected] Petr Kulish Russian Academy of Sciences Steklov Institute of Mathematics St. Petersburg Russia 191023 [email protected] Julius Wess Arnold Sommerfeld Centre for Theoretical Physics Theresienstr. 37 80333 M¨unchen and II Institut f¨ur Theoretische Physik and DESY Luruper Chaussee 149 22761 Hamburg Germany [email protected] [email protected]

Marija Dimitrijevi´c INFN Sezione di Torino Gruppo Collegato di Alessandria Via Teresa Michel 11 15100 Alessandria Italy and Faculty of Physics University of Belgrade P.O. Box 368 11001 Beograd Serbia [email protected] Fedele Lizzi Universit´a di Napoli Federico II and INFN, Sezione di Napoli Via Cintia 80126 Napoli Italy [email protected]

Aschieri, P. et al., Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory, Lect. Notes Phys. 774 (Springer, Berlin Heidelberg 2009), DOI 10.1007/978-3-540-89793-4 Lecture Notes in Physics ISSN 0075-8450 e-ISSN 1616-6361 ISBN 978-3-540-89792-7 e-ISBN 978-3-540-89793-4 DOI 10.1007/978-3-540-89793-4 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009921271 c Springer-Verlag Berlin Heidelberg 2009  T