Noncommutative Differential Geometry and Its Applications to Physics

by Maeda, Yoshiaki; Moriyoshi, Hitoshi; Omori, Hideki; Sternheimer, Daniel; Tate, Tatsuya

• ISBN13: 9780792369301
• ISBN10: 0792369300
• Format: Hardcover
• Copyright: 2001-04-01
• Publisher: Kluwer Academic Pub

Summary

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 hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

Table of Contents

Preface	vii
Methods of Equivariant Quantization	1	(12)
Christian Duval
Pierre B. A. Lecomete
Valentin Ovsienko
Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory	13	(18)
Takanori Fujiwara
Hiroshi Suzuki
Ke Wu
Geometrical Structures on Noncommutative Spaces	31	(18)
Olivier Grandjean
A Relation Between Commutative and Noncommutative Descriptions of D-Branes	49	(14)
Nobuyuki Ishibashi
Intersection Numbers On The Moduli Spaces of Stable Maps in Genus O	63	(36)
Alexandre Kabanov
Takashi Kimura
D-Brane Actions on Kahler Manifolds	99	(24)
Akishi Kato
On the Projective Classification of The Modules of Differential Operators on Rm	123	(8)
Pierre B. A. Lecomte
An Interpretation of Schouten-Nijenhuis Bracket	131	(14)
Kentaro Mikami
Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators	145	(10)
Naoya Miyazaki
C*-Algebraic Deformation and Index Theory	155	(14)
Toshikazu Natsume
Singular Systems of Exponential Functions	169	(18)
Hideki Omori
Yoshiaki Maeda
Naoya Miyazaki
Akira Yoshioka
Determinats of Elliptic Boundary Problems in Quantum Field Theory	187	(30)
Simon G. Scott
Krzysztov P. Wojciechowski
On Geometry of Non-Abelian Duality	217	(10)
Pavol Severa
Weyl Calculus and Wigner Transform on the Poincare Disk	227	(18)
Tatsuya Tate
Lectures on Graded Differential Algebras and Noncommutative Geometry	245
Michel Dubois-Violette