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From classical trajectories to quantum commutation relations

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URI: https://hdl.handle.net/10016/35828
ISBN: 978-3-030-24747-8
DOI: https://doi.org/10.1007/978-3-030-24748-5_9
UXXI: CC/0000032915
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Classical_SPIP_2019_cc_ps.pdf (650.87 KB)
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2018-03-05
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Springer
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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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Ciaglia, F. M., Marmo, G. & Schiavone, L. (2019). From Classical Trajectories to Quantum Commutation Relations. Springer Proceedings in Physics, 163-185
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