Preface -- Contents -- Chapter 1 Diffeomorphism Groups and Quantum Configurations -- 1.1 Diffeomorphism Groups and Physical Space -- 1.2 Diffeomorphism Group Representations and Quantum Mechanics -- 1.3 Causal Diffeomorphisms and Space-Time -- 1.4 Diffeomorphism Groups and Particle Configurations -- 1.5 Unitary Representations: Quasi-invariant Measures and Cocycles -- 1.6 Comments on Quantization -- 1.7 Deriving Brackets for Creation and Annihilation Fields -- 1.8 Infinite Dimensional Configuration Spaces -- Bibliography -- Chapter 2 Functorial Quantization and the Guillemin-Sternberg Conjecture -- 2.1 Introduction -- 2.2 Classical Reduction -- 2.3 Symplectic Dual Pairs as Arrows -- 2.4 The Guillemin-Sternberg Conjecture -- 2.5 Spinc Structures and Dirac Operators -- 2.6 Bott's Definition of Quantization -- 2.7 From Quantization to KK-Theory -- 2.8 Kasparov Bimodules as Arrows -- 2.9 The Guillemin-Sternberg Conjecture Revisited -- 2.10 Guillemin-Sternberg for Noncompact Groups -- 2.11 Foliation Theory and Quantization -- Bibliography -- Chapter 3 Coherent State Method in Geometric Quantization -- 3.1 Introduction -- 3.2 Coherent State Map -- 3.3 Different Representations of Mechanical Systems -- 3.4 Kostant-Souriau Prequantization and Positive Hermitian Kernels -- 3.5 Relation Between Classical and Quantum Observables -- 3.6 Examples -- Acknowledgements -- Bibliography -- Chapter 4 The Group of Volume Preserving Diffeomorphisms and the Lie Algebra of Unimodular Vector Fields: Survey of Some Classical and Not-so-classical Results -- 4.1 Introduction -- Basic definitions and forewords -- 4.2 Some Results on the Cohomology of the Lie Algebra of Unimodular Vector Fields -- 4.3 More Results about Cohomology of Lie Algebra of Unimodular Vector Fields: The Rigidity Theorem -- 4.4 Unimodular Vector Fields in Supergeometry.

4.5 About the Group of Volume Preserving Diffeomorphisms -- 4.6 About Coadjoint Orbits of SD(V) and its Central Extensions -- Bibliography -- Chapter 5 Moduli Space of Germs of Symplectic Connections of Ricci Type -- 5.1 Introduction -- 5.2 Some Properties of Ricci Type Connections -- 5.3 Examples of Manifolds with Ricci Type Connections -- 5.4 Complex Projective Space -- Bibliography -- Chapter 6 Banach Lie-Poisson Spaces -- 6.1 Introduction -- 6.2 Banach Lie-Poisson spaces -- 6.3 Examples of Banach Lie-Poisson Spaces -- 6.4 Coadjoint Orbits -- Acknowledgments -- Bibliography -- Chapter 7 Spectra of Operators Associated with Dynamical Systems: From Ergodicity to the Duality Principle -- 7.1 Introduction. Operators Associated with Dynamical Systems: Shifts and Weighted Shifts. Some Historical Notes and Problems -- 7.2 Dynamical Nature of the Spectrum of Operators with Invertible Shifts: Spectral Radius and Ergodic Measures -- 7.3 Dynamical Nature of the Spectral Radius of Operators with Irreversible Shifts - First Steps: Spectral Radius and Topological Pressure -- 7.4 Dynamical Nature of the Spectral Radius of Operators with Irreversible Shifts - Present State: The Duality Principle -- 7.5 Perron-Frobenius Dynamical Systems -- Bibliography -- Chapter 8 An Ergodic Arnold-Liouville Theorem for Locally Symmetric Spaces -- 8.1 Invariant Vector Fields on Homogeneous Spaces -- 8.2 Tangent Bundles of Symmetric Spaces -- 8.3 Commuting Vector Fields and Flows -- 8.4 The Ergodic Arnold-Liouville Theorem -- Bibliography -- Chapter 9 The Renormalization Fixed Point as a Mathematical Object -- 9.1 Introduction -- 9.2 Percolation -- 9.3 The Ising Model -- 9.4 Possible Construction of a Conformal Field Theory -- 9.5 Calculations for the Symmetric Group -- 9.6 Final Remarks -- Bibliography -- Chapter 10 A Cohomological Description of Abelian Bundles and Gerbes.

10.1 Introduction -- Acknowledgements -- 10.2 The Local Equations for Bundles with Connection -- 10.3 The Generalisation to Gerbes with Connection and an Example -- 10.4 A Cohomological Formulation -- 10.5 Comments -- Bibliography -- Chapter 11 On a Quantum Group of Unitary Operators: The Quantum 'az + b' Group -- 11.1 Introduction -- 11.2 Group , Related Special Functions and Generating Algebras -- 11.3 Construction of Quantum 'az + b' Group -- Acknowledgement -- Bibliography.