Quantization of Singular Symplectic Quotients

N.P. Landsman, Markus Pflaum, Martin Schlichenmaier (Herausgeber)

Buch | Softcover

XII, 355 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 2001
Springer Basel (Verlag)
978-3-0348-9535-4 (ISBN)

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lt;p>This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. 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 field.

Some comments on the history, theory, and applicationsof symplectic reduction.- Homology of complete symbols and non-commutative geometry.- Cohomology of the Mumford quotient.- Poisson sigma models and symplectic groupoids.- Pseudo-differential operators and deformation quantization.- Singularities and Poisson geometry of certainrepresentation spaces.- Quantized reduction as a tensor product.- Analysis of geometric operator on open manifolds: a groupoid approach.- Smooth structures on stratified spaces.- Singular projective varieties and quantization.- Poisson structure and quantization of Chern-Simons theory.- Combinatorial quantization of Euclidean gravityin three dimensions.- The Yang-Mills measure and symplectic structureover spaces of connections.

Erscheint lt. Verlag	1.11.2012
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XII, 355 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	561 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	area • cohomology • Geometry • Homology • Mathematical Physics • Topology
ISBN-10	3-0348-9535-6 / 3034895356
ISBN-13	978-3-0348-9535-4 / 9783034895354
Zustand	Neuware