Chapter

Symmetries in Science X

pp 223-284

From Equations of Motion to Canonical Commutation Relations: Classical and Quantum Systems

  • V. I. Man’koAffiliated withDipartimento di Scienze Fisiche, Universitá di Napoli “Federico II”, Instituto Nazionale di Fisica Nucleare, Sezione di NapoliLebedev Physical Institute
  • , G. MarmoAffiliated withDipartimento di Scienze Fisiche, Universitá di Napoli “Federico II”, Instituto Nazionale di Fisica Nucleare, Sezione di Napoli
  • , F. ZaccariaAffiliated withDipartimento di Scienze Fisiche, Universitá di Napoli “Federico II”, Instituto Nazionale di Fisica Nucleare, Sezione di Napoli

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Abstract

We consider equations of motion for classical and quantum systems. It is shown that they do not determine uniquely the canonical commutation relations, neither at the classical level, nor at the quantum level. By using some of the alternative commutation relations as deformed ones, we consider the description of deformed systems, classical and quantum. In particular, by using deformed oscillators we deal with photon statistics in nonlinear coherent states and possible influence of deformations on electrostatics.