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The Resource Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource)
Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource)
Resource Information
The item Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 superintegrability, 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 ''allinclusive'' 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
 Language
 eng
 Extent
 XXV, 719 p. 22 illus.
 Contents

 Contents
 Foreword
 Some examples of linear and nonlinear physical systems and their dynamical equations
 The language of geometry and dynamical systems: the linearity paradigm
 The geometrization of dynamical systems
 Invariant structures for dynamical systems: Poisson and Jacobi dynamics
 The classical formulations of dynamics of Hamilton and Lagrange
 The geometry of Hermitean spaces: quantum evolution
 Folding and unfolding Classical and Quantum systems
 Integrable and superintegrable systems
 LieScheffers systems
 Appendices
 Bibliography
 Index
 Isbn
 9789401792202
 Label
 Geometry from Dynamics, Classical and Quantum
 Title
 Geometry from Dynamics, Classical and Quantum
 Statement of responsibility
 by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi
 Language
 eng
 Summary
 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 superintegrability, 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 ''allinclusive'' 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
 http://library.link/vocab/creatorName
 Cariñena, José F
 Image bit depth
 0
 LC call number
 QC19.220.85
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Ibort, Alberto.
 Marmo, Giuseppe.
 Morandi, Giuseppe.
 SpringerLink
 http://library.link/vocab/subjectName

 Physics
 Global differential geometry
 Mechanics
 Physics
 Theoretical, Mathematical and Computational Physics
 Mathematical Physics
 Statistical Physics, Dynamical Systems and Complexity
 Differential Geometry
 Mechanics
 Label
 Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Contents  Foreword  Some examples of linear and nonlinear physical systems and their dynamical equations  The language of geometry and dynamical systems: the linearity paradigm  The geometrization of dynamical systems  Invariant structures for dynamical systems: Poisson and Jacobi dynamics  The classical formulations of dynamics of Hamilton and Lagrange  The geometry of Hermitean spaces: quantum evolution  Folding and unfolding Classical and Quantum systems  Integrable and superintegrable systems  LieScheffers systems  Appendices  Bibliography  Index
 Dimensions
 unknown
 Extent
 XXV, 719 p. 22 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789401792202
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789401792202
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789401792202
 Label
 Geometry from Dynamics, Classical and Quantum, by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Contents  Foreword  Some examples of linear and nonlinear physical systems and their dynamical equations  The language of geometry and dynamical systems: the linearity paradigm  The geometrization of dynamical systems  Invariant structures for dynamical systems: Poisson and Jacobi dynamics  The classical formulations of dynamics of Hamilton and Lagrange  The geometry of Hermitean spaces: quantum evolution  Folding and unfolding Classical and Quantum systems  Integrable and superintegrable systems  LieScheffers systems  Appendices  Bibliography  Index
 Dimensions
 unknown
 Extent
 XXV, 719 p. 22 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789401792202
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789401792202
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789401792202
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