| 书目名称 | Geometry from Dynamics, Classical and Quantum | | 编辑 | José F. Cariñena,Alberto Ibort,Giuseppe Morandi | | 视频video | | | 概述 | The interplay between geometry and physics is presented in a novel way: geometrical structures are derived from dynamics.Simple examples are given to simplify abstract and difficult geometrical ideas | | 图书封面 |  | | 描述 | 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 | | 出版日期 | Book 2015 | | 关键词 | Integrable Systems; Invariant Hermitean Structures; Inverse Problems; Kaehler Manifolds; Kustaanheimo-St | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-9220-2 | | isbn_softcover | 978-94-024-0154-7 | | isbn_ebook | 978-94-017-9220-2 | | copyright | Springer Science+Business Media Dordrecht 2015 |
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发表于 2025-3-21 16:09:26
