Noncommutative Differential Geometry and Its Applications to Physics
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to
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MATHEMATICAL PHYSICS STUDIES Editorial Board:
Maxim Kontsevich, IHES, Bures-sur- Yvette, France Massimo Porrati, New York University, New York, US.A. Jacques Simon, Universite Bourgogne, Dijon, France Daniel Sternheimer, Universite Bourgogne, Dijon, France
VOLUME 23
Noncommutative Differential Geometry and Its Applications to Physics Proceedings of the Workshop at Shonan, Japan, June 1999
Edited by
Yoshiaki Maeda Keio UniversilY, Yokohama, Japan
Hitoshi Moriyoshi Keio Universily, Yokohama, Japan
Hideki Omori Science Universily of Tokyo, Noda, Japan
Daniel Stemheimer CNRS and Universill? de Bourgogne, Dijon, France
Tatsuya Tate Keio UniversilY, Yokohama, Japan and
Satoshi Watamura Tohoku UniversilY, Sendai, Japan
Springer-Science+Business Media, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-3829-4 ISBN 978-94-010-0704-7 (eBook) DOI 10.1007/978-94-010-0704-7
Printed on acid-free paper
AII Rights Reserved © 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint ofthe hardcover Ist edition 2001 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, incIuding photocopying, recording or by any information storage and retrieval system, without written permis sion from the copyright owner.
TABLE OF CONTENTS
PREFACE
vii
METIIODS OF EQUIVARIANT QUANTIZATION Christian Duval, Pierre B.A. Lecomte and Valentin Ovsienko APPLICATION OF NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON LATI1CE TO ANOMALY ANALYSIS IN ABELIAN LATI1CE GAUGE THEORY Takanori Fujiwara, Hiroshi Suzuki and Ke Wu
13
GEOMETRICAL STRUCTURES ON NONCOMMUTATIVE SPACES Olivier Grandjean
31
A RELATION BETWEEN COMMUTATIVE AND NONCOMMUTATIVE DESCRIPTIONS OF D-BRANES Nobuyuki Ishibashi
49
INTERSECTION NUMBERS ON THE MODULI SPACES OF STABLE MAPS IN GENUS 0 Alexandre Kabanov and Takashi Kimura
63
D-BRANE ACTIONS ON KAHLER MANIFOLDS Akishi Kato
99
ON TIlE PROJECTIVE CLASSIFICATION OF THE MODULES OF DIFFERENTIAL OPERATORS ON IRm Pierre B. A. Lecomte
123
AN INTERPRETATION OF SCHOUTEN-NIJENHUIS BRACKET Kentaro Mikami
131
v
Vi
NONCOMMUTATIVE DIFFERENTIAL GEOMETRY
REMARKS ON THE CHARACTERISTIC CLASSES ASSOCIATED WITH THE GROUP OF FOURIER INTEGRAL OPERATORS Naoya Miyazaki
145
C* -ALGEBRAIC DEFORMATION AND INDEX THEORY
155
Toshikazu Natsume
SINGULAR SYSTEMS OF EXPONENTIAL FUNCTIONS Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka
169
DETERMINANTS OF ELLIPTIC BOUNDARY PROBLEMS IN QUANTUM FIELD THEORY Simon G. Scott and Krzysztov P. Wojciechowski
187
ON GEOMETRY OF NON-ABELIAN DUALITY Pavol Severa
217
WEYL CALCULUS AND WIGNER TRANSFORM ON THE POINCARE DISK Tatsuya Tate
227
LECTURES ON GRADED DIFFERENTIAL ALGEBRAS AND NONCOMMUTATIVE GEOMETRY Michel Dubois- Violette
245
PREFACE
A workshop on "noncommutative differential geometry and its applications to physics" was held at Shonan International Village at Ha
