2019/01/01 by Florio M. Ciaglia, G. Marmo, Giuseppe Marmo +1
Mathematics · Physics and Astronomy · #Classical mechanics #Differential equation #Dynamical systems theory #Hamiltonian (control theory) #Ingenuity #Lagrangian #Mathematical optimization #Mathematical physics #Mathematics #Noether's theorem #Nonlinear Waves and Solitons #Numerical methods for differential equations #Philosophy #Physics #Quantization (signal processing) #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Theoretical physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/978-3-030-24748-5_9
published as Springer Proceedings in Physics, volume 229, 2019 · 25 pages. Comments are welcome!
openalex publication_date 2019/01/01 · arxiv created 2019/08/19 · arxiv updated 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.