Hamiltonian Mechanical Systems and Geometric Quantization - Couverture souple

Puta, Mircea

 
9789401048804: Hamiltonian Mechanical Systems and Geometric Quantization
Couverture souple
ISBN 10 : 9401048800 ISBN 13 : 9789401048804
Editeur : Springer, 2012

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2012
Langue
anglais
ISBN 10 
9401048800
ISBN 13 
9789401048804
Reliure
Broché
Nombre de pages
292
Coordonnées du fabricant
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Poststr. 9
Darmstadt
64293
Allemagne

Autres éditions populaires du même titre

9780792323068: Hamiltonian Mechanical Systems and Geometric Quantization

Edition présentée

ISBN 10 :  0792323068 ISBN 13 :  9780792323068
Editeur : Kluwer Academic Publishers, 1993
Couverture rigide