edited by S Twareque Ali (Concordia University, Canada) , Gerard G Emch (University of Florida, USA) , Anatol Odzijewicz (University of Bialystok, Poland) , Martin Schlichenmaier (Université du Luxembourg, Luxembourg) , & Stanislaw L Woronowicz (University of Warsaw, Poland)

Table of Contents (28k)
Preface (219k)
Chapter 1: Diffeomorphism Groups and Quant um Configurations (805k)

This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1-7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience.

This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view.

• Aspects of Quantization:
  • Diffeomorphism Groups and Quantum Configurations (G A Goldin)
  • Functorial Quantization and the Guillemin–Sternberg Conjecture (N P Landsman)
  • Coherent State Method in Geometric Quantization (A Odzijewicz)
  • The Group of Volume Preserving Diffeomorphisms and the Lie Algebra of Unimodular Vector Fields: Survey of Some Classical and Not-So-Classical Results (C Roger)
• Symplectic and Poisson Geometry:
  • Moduli Space of Germs of Symplectic Connections of Ricci Type (M Cahen)
  • Banach Lie–Poisson Spaces (A Odzijewicz & T S Ratiu)
• Other Mathematical Methods:
  • Spectra of Operators Associated with Dynamical Systems: From Ergodicity to the Duality Principle (A B Antonevich et al.)
  • An Ergodic Arnold-Liouville Theorem for Locally Symmetric Spaces (J Hilgert)
  • The Renormalization Fixed Point as a Mathematical Object (R P Langlands)
  • A Cohomological Description of Abelian Bundles and Gerbes (R Picken)
  • On a Quantum Group of Unitary Operators: The Quantum az + b Group (W Pusz & S L Woronowicz)