2017/05/26 by Claudia Maria Chanu, Giovanni Rastelli · 6 citations
Mathematics · Physics and Astronomy · #Coupling constant #Factorization #Hamiltonian (control theory) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Polynomial #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Structure constants #math-ph #math.MP #msc:70H06 #msc:81R12 #msc:81R15 #msc:81S05 #quant-ph
paper · pdf · doi:10.1016/j.aop.2017.09.001
published in Annals of Physics 386, 254-274 (Elsevier BV) · 25 pages
arxiv created 2017/05/26 · openalex publication_date 2017/09/23 · arxiv updated 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in the family of extended Hamiltonians, geometrically characterized by the structure of warped manifold of their configuration manifold. For the extended manifolds, the characteristic constants of motion of high degree are polynomial in the momenta of determined form. We consider here a different form of the constants of motion, based on the factorization procedure developed by S. Kuru, J. Negro and others. We show that an important subclass of the extended Hamiltonians admits factorized constants of motion and we determine their expression. The classical constants may be non-polynomial in the momenta, but the factorization procedure allows, in a type of extended Hamiltonians, their quantization via shift and ladder operators, for systems of any finite dimension.