Ebook: Quantization of Singular Symplectic Quotients

This is the first exposition of the quantization theory of singular symplectic (i.e., Marsden-Weinstein) quotients and their applications to physics in book form. A preface by J. Marsden and A. Weinstein precedes individual refereed contributions by M.T. Benameur and V. Nistor, M. Braverman, A. Cattaneo and G. Felder, B. Fedosov, J. Huebschmann, N.P. Landsman, R. Lauter and V. Nistor, M. Pflaum, M. Schlichenmaier, V. Schomerus, B. Schroers, and A. Sengupta. This book is intended for mathematicians and mathematical physicists working in quantization theory, algebraic, symplectic, and Poisson geometry, the analysis and geometry of stratified spaces, pseudodifferential operators, low-dimensional topology, operator algebras, noncommutative geometry, or Lie groupoids, and for theoretical physicists interested in quantum gravity and topological quantum field theory. The subject matter provides a remarkable area of interaction between all these fields, highlighted in the example of the moduli space of flat connections, which is discussed in detail. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this fascinating and expanding field, or enter it oneself. It is to be expected that the quantization of singular spaces will become a key theme in 21st century (concommutative) geometry.

---

---

Content:
Front Matter....Pages i-xii
Comments on the history, theory, and applications of symplectic reduction....Pages 1-19
Homology of complete symbols and noncommutative geometry....Pages 21-46
Cohomology of the Mumford quotient....Pages 47-59
Poisson sigma models and symplectic groupoids....Pages 61-93
Pseudo-differential operators and deformation quantization....Pages 95-118
Singularities and Poisson geometry of certain representation spaces....Pages 119-135
Quantized reduction as a tensor product....Pages 137-180
Analysis of geometric operators on open manifolds: A groupoid approach....Pages 181-229
Smooth structures on stratified spaces....Pages 231-258
Singular projective varieties and quantization....Pages 259-282
Poisson structure and quantization of Chern-Simons theory....Pages 283-305
Combinatorial quantization of Euclidean gravity in three dimensions....Pages 307-327
The Yang-Mills measure and symplectic structure over spaces of connections....Pages 329-355

---

Content:
Front Matter....Pages i-xii
Comments on the history, theory, and applications of symplectic reduction....Pages 1-19
Homology of complete symbols and noncommutative geometry....Pages 21-46
Cohomology of the Mumford quotient....Pages 47-59
Poisson sigma models and symplectic groupoids....Pages 61-93
Pseudo-differential operators and deformation quantization....Pages 95-118
Singularities and Poisson geometry of certain representation spaces....Pages 119-135
Quantized reduction as a tensor product....Pages 137-180
Analysis of geometric operators on open manifolds: A groupoid approach....Pages 181-229
Smooth structures on stratified spaces....Pages 231-258
Singular projective varieties and quantization....Pages 259-282
Poisson structure and quantization of Chern-Simons theory....Pages 283-305
Combinatorial quantization of Euclidean gravity in three dimensions....Pages 307-327
The Yang-Mills measure and symplectic structure over spaces of connections....Pages 329-355
....