From Classical Trajectories to Quantum Commutation Relations

  • F. M. Ciaglia
  • G. Marmo
  • L. SchiavoneEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 229)


In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.


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Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Dipartimento di Fisica “E. Pancini”Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6via CintiaItaly
  3. 3.Department of Mathematics, Faculty of ScienceUniversity of OstravaOstravaCzech Republic

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