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Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures
Author(s) -
Aldaya Victor,
De Azcárraga José A.
Publication year - 1987
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190350602
Subject(s) - mathematics , dynamical systems theory , quantum , hamiltonian (control theory) , hamiltonian system , group (periodic table) , classical limit , manifold (fluid mechanics) , order (exchange) , mathematical physics , physics , quantum mechanics , mathematical optimization , mechanical engineering , engineering , finance , economics
This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton‐Jacobi theory and other problems such as the definition and globalization of the Poincaré‐Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different structures appearingin the theory are provided, including a treatment of constrained and generalized higher order dynamical systems.