Hamiltonian Mechanical Systems and Geometric Quantization

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Hamiltonian Mechanical Systems and Geometric ...
Mircea Puta
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January 31, 2024 | History

Hamiltonian Mechanical Systems and Geometric Quantization

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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.

Publish Date
Publisher
Island Press
Language
English

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Edition Availability
Cover of: Hamiltonian Mechanical Systems and Geometric Quantization
Hamiltonian Mechanical Systems and Geometric Quantization
2012, Springer
in English
Cover of: Hamiltonian Mechanical Systems and Geometric Quantization
Hamiltonian Mechanical Systems and Geometric Quantization
Nov 05, 2012, Springer
paperback
Cover of: Hamiltonian Mechanical Systems and Geometric Quantization
Hamiltonian Mechanical Systems and Geometric Quantization
1993, Island Press
in English
Cover of: Hamiltonian mechanical systems and geometric quantization
Hamiltonian mechanical systems and geometric quantization
1993, Kluwer Academic Publishers
in English

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Book Details


The Physical Object

Pagination
292
Weight
0.414

ID Numbers

Open Library
OL50683220M
ISBN 13
9789401119931

Source records

Better World Books record

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January 31, 2024 Created by ImportBot Imported from Better World Books record