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Symplectic Geometry and Quantization
Edited by: Yoshiaki Maeda, Hideki Omori, and Alan Weinstein

Contemporary Mathematics
1994; 285 pp; softcover
Volume: 179
ISBN-10: 0-8218-0302-6
ISBN-13: 978-0-8218-0302-8
List Price: US$63
Member Price: US$50.40
Order Code: CONM/179
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This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants. The book provides insight into how these different topics relate to one another and offers intriguing new problems. Providing a look at the frontier of research in symplectic geometry and quantization, this book is suitable as a source book for a seminar in symplectic geometry.


Graduate students and researchers

Table of Contents

  • M. Cahen, S. Gutt, and J. Rawnsley -- Some remarks on the classification of Poisson Lie groups
  • P. Dazord -- Lie groups and algebras in infinite dimension: A new approach
  • J. J. Duistermaat -- Equivariant cohomology and stationary phase
  • E. Getzler -- The Bargmann representation, generalized Dirac operators, and the index of pseudodifferential operators on \(\mathbb R^{n}\)
  • M. Karasev -- Quantization by means of two-dimensional surfaces (membranes): Geometrical formulas for wave-functions
  • T. Kohno -- Vassiliev invariants and de Rham complex on the space of knots
  • H. Konno -- Geometry of loop groups and Wess-Zumino-Witten models
  • T. Masuda and H. Omori -- The noncommutative algebra of the quantum group \(SU_q(2)\) as a quantized Poisson manifold
  • K. Mikami -- Symplectic and Poisson structures on some loop groups
  • H. Moriyoshi -- The Euler and Godbillon-Vey forms and symplectic structures on \(Dif\, f_+^\infty (S^1)/SO(2)\)
  • Y. Nakamura -- A Tau-function for the finite Toda molecule, and information spaces
  • H. Omori, Y. Maeda, and A. Yoshioka -- Deformation quantizations of Poisson algebras
  • K. Ono and S. Stolz -- An analogue of Edmonds' theorem for loop spaces
  • A. Weinstein -- Traces and triangles in symmetric symplectic spaces
  • S. Zakrzewski -- Geometric quantization of Poisson groups--Diagonal and soft deformations
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