Hamiltonian Mechanical Systems And Geometric Quantization

Author : Mircea Puta
Publisher : Unknown
Page : 292 pages
File Size : 45,8 Mb
Release : 1993-06-30
Category : Electronic
ISBN : 9401119937

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Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta Pdf

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.

Author : Mircea Puta
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401119924

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Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814464550

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Geometric Formulation of Classical and Quantum Mechanics by Anonim Pdf

Author : G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili
Publisher : World Scientific
Page : 405 pages
File Size : 45,7 Mb
Release : 2011
Category : Science
ISBN : 9789814313728

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Geometric Formulation of Classical and Quantum Mechanics by G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili Pdf

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.

Author : S Twareque Ali,Anatol Odzijewicz,I M Mladenov
Publisher : World Scientific
Page : 256 pages
File Size : 48,5 Mb
Release : 1993-10-29
Category : Electronic
ISBN : 9789814522038

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Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics by S Twareque Ali,Anatol Odzijewicz,I M Mladenov Pdf

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.

Author : Syed Twareque Ali,Ivailo M. Mladenov,A. Odzijewicz
Publisher : World Scientific Publishing Company Incorporated
Page : 244 pages
File Size : 48,6 Mb
Release : 1993-01-01
Category : Science
ISBN : 9810214472

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Quantization and Coherent States Methods by Syed Twareque Ali,Ivailo M. Mladenov,A. Odzijewicz Pdf

Author : Nicholas Michael John Woodhouse
Publisher : Oxford University Press
Page : 324 pages
File Size : 41,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0198502702

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Geometric Quantization by Nicholas Michael John Woodhouse Pdf

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.

Author : Jedrzej Sniatycki
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461260660

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Geometric Quantization and Quantum Mechanics by Jedrzej Sniatycki Pdf

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.

Author : G. Giachetta,L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili
Publisher : World Scientific
Page : 716 pages
File Size : 46,8 Mb
Release : 2005
Category : Science
ISBN : 9789812561299

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Geometric and Algebraic Topological Methods in Quantum Mechanics by G. Giachetta,L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili Pdf

- The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.

Author : Alfredo M. Ozorio de Almeida
Publisher : Cambridge University Press
Page : 262 pages
File Size : 52,5 Mb
Release : 1988
Category : Mathematics
ISBN : 0521386705

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Hamiltonian Systems by Alfredo M. Ozorio de Almeida Pdf

Hamiltonian Systems outlines the main results in the field, and considers the implications for quantum mechanics.

Author : David John Simms,Nicholas Michael John Woodhouse
Publisher : Springer
Page : 188 pages
File Size : 40,7 Mb
Release : 1976
Category : Science
ISBN : UOM:39015057383286

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Lectures on Geometric Quantization by David John Simms,Nicholas Michael John Woodhouse Pdf

Author : Alexander Cardona,Pedro Morales,Hernán Ocampo,Sylvie Paycha,Andrés F. Reyes Lega
Publisher : Springer
Page : 341 pages
File Size : 52,5 Mb
Release : 2017-10-26
Category : Science
ISBN : 9783319654270

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Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by Alexander Cardona,Pedro Morales,Hernán Ocampo,Sylvie Paycha,Andrés F. Reyes Lega Pdf

This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662067932

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Dynamical Systems IV by V.I. Arnol'd,S.P. Novikov Pdf

This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.

Author : Kang Feng,Mengzhao Qin
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 45,7 Mb
Release : 2010-10-18
Category : Mathematics
ISBN : 9783642017773

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Symplectic Geometric Algorithms for Hamiltonian Systems by Kang Feng,Mengzhao Qin Pdf

"Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.

Author : Paul Lee Robinson,John Howard Rawnsley
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 53,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821824733

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The Metaplectic Representation, $Mp^c$ Structures and Geometric Quantization by Paul Lee Robinson,John Howard Rawnsley Pdf