Geometry from Dynamics, Classical and Quantum

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is...

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Những tác giả chính:	Carinena, J.F, Ibort, A, Marmo, G, Morandi, G
Định dạng:	Sách
Ngôn ngữ:	English
Được phát hành:	Springer 2015
Những chủ đề:	Physics Mathematical physics Geometric quantization
Truy cập trực tuyến:	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58240
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spelling	oai:scholar.dlu.edu.vn:DLU123456789-582402023-11-11T06:04:48Z Geometry from Dynamics, Classical and Quantum Carinena, J.F Ibort, A Marmo, G Morandi, G Physics Mathematical physics Geometric quantization This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics. 2015-09-14T06:42:56Z 2015-09-14T06:42:56Z 2015 Book 978-94-017-9220-2 978-94-017-9219-6 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58240 en application/pdf Springer
institution	Thư viện Trường Đại học Đà Lạt
collection	Thư viện số
language	English
topic	Physics Mathematical physics Geometric quantization
spellingShingle	Physics Mathematical physics Geometric quantization Carinena, J.F Ibort, A Marmo, G Morandi, G Geometry from Dynamics, Classical and Quantum
description	This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
format	Book
author	Carinena, J.F Ibort, A Marmo, G Morandi, G
author_facet	Carinena, J.F Ibort, A Marmo, G Morandi, G
author_sort	Carinena, J.F
title	Geometry from Dynamics, Classical and Quantum
title_short	Geometry from Dynamics, Classical and Quantum
title_full	Geometry from Dynamics, Classical and Quantum
title_fullStr	Geometry from Dynamics, Classical and Quantum
title_full_unstemmed	Geometry from Dynamics, Classical and Quantum
title_sort	geometry from dynamics, classical and quantum
publisher	Springer
publishDate	2015
url	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58240
_version_	1782533009021337600

Geometry from Dynamics, Classical and Quantum

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