
Geometry from Dynamics, Classical and Quantum
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Reviews / Votes
"This impressive book takes the reader onto a long journey through the topological and geometrical settings behind the main topics of classical and quantum mechanics. . The book is completely self-contained, besides from references to the original literature (every chapter finishes with a reference list), for all of the presented results also the proofs are given. . Reading this book provides an excellent opportunity to practice and understand the geometric mechanics." (Mircea Crâsmareanu, zbMATH 1364.81001, 2017)
"It is offered for a comprehensive exposition of the use of geometrical tools in the study of both classical and quantum systems. It would be very useful to a motivated student or a researcher wishing to adopt the geometrical framework in his/her work. Each chapter contains an extensive bibliography, old and current, doing justice to the various possible directions of study." (Demetris P. K. Ghikas, Mathematical Reviews, October, 2015)
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Content
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.- Lie-Scheffers systems.- Appendices.- Bibliography.- Index.