Hamiltonian Mechanical Systems And Geometric Quantization
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Hamiltonian Mechanical Systems and Geometric Quantization
Author | : Mircea Puta |
Publsiher | : Unknown |
Total Pages | : 292 |
Release | : 1993-06-30 |
Genre | : Electronic Book |
ISBN | : 9401119937 |
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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.
Hamiltonian Mechanical Systems and Geometric Quantization
Author | : Mircea Puta |
Publsiher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9789401119924 |
Download Hamiltonian Mechanical Systems and Geometric Quantization Book in PDF, Epub and Kindle
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.
Geometric Formulation of Classical and Quantum Mechanics
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9789814464550 |
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Geometric Formulation of Classical and Quantum Mechanics
Author | : G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili |
Publsiher | : World Scientific |
Total Pages | : 405 |
Release | : 2011 |
Genre | : Science |
ISBN | : 9789814313728 |
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The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
Quantization And Coherent States Methods Proceedings Of Xi Workshop On Geometric Methods In Physics
Author | : S Twareque Ali,Anatol Odzijewicz,I M Mladenov |
Publsiher | : World Scientific |
Total Pages | : 256 |
Release | : 1993-10-29 |
Genre | : Electronic Book |
ISBN | : 9789814522038 |
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The aim of the conference was to find common elements between quantization and coherent states, and quantization on Poisson manifolds. Topics included are coherent states, geometric quantization, phase space quantization, deformation and *-products and Berry's phase.
Quantization and Coherent States Methods
![Quantization and Coherent States Methods](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Syed Twareque Ali,Ivailo M. Mladenov,A. Odzijewicz |
Publsiher | : World Scientific Publishing Company Incorporated |
Total Pages | : 244 |
Release | : 1993-01-01 |
Genre | : Science |
ISBN | : 9810214472 |
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Geometric Quantization
Author | : Nicholas Michael John Woodhouse |
Publsiher | : Oxford University Press |
Total Pages | : 324 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 0198502702 |
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The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
Geometric Quantization and Quantum Mechanics
Author | : Jedrzej Sniatycki |
Publsiher | : Springer Science & Business Media |
Total Pages | : 241 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9781461260660 |
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This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.