Hamiltonian Mechanical Systems and Geometric Quantization (Mathematics and Its Applications, Band 260) - Softcover

Puta, Mircea

Softcover

ISBN 10: 9401048800 ISBN 13: 9789401048804

Verlag: Springer, 2012

Inhaltsangabe

This volume presents various aspects of the geometry of symplectic and Poisson manifolds, and applications in Hamiltonian mechanics and geometric quantization are indicated.
Chapter 1 presents some general facts about symplectic vector space, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. Chapter 3 considers some standard facts concerning Lie groups and algebras which lead to the theory of momentum mappings and the Marsden--Weinstein reduction. Chapters 4 and 5 consider the theory and the stability of equilibrium solutions of Hamilton--Poisson mechanical systems. Chapters 6 and 7 are devoted to the theory of geometric quantization. This leads, in Chapter 8, to topics such as foliated cohomology, the theory of the Dolbeault--Kostant complex, and their applications. A discussion of the relation between geometric quantization and the Marsden--Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic groupoids.
Each chapter concludes with problems and solutions, many of which present significant applications and, in some cases, major theorems.
For graduate students and researchers whose interests and work involve symplectic geometry and Hamiltonian mechanics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 9401048800
• ISBN 13: 9789401048804
• Einband: Taschenbuch
• Anzahl der Seiten: 292
• Kontakt zum Hersteller: Nicht verfügbar
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