2010/11/30 by Guowu Meng
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Orbital Angular Momentum in Optics #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.7546/jgsp-36-2014-47-57
published as J. Geom. Symm. Phys. {\bf 36} (2014) 47-57 · 8 pages
openalex publication_date 2014/01/01 · arxiv created 2014/12/04 · arxiv updated 2014/12/12 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
For each simple euclidean Jordan algebra V !, we introduce the\nanalogue of hamiltonian, angular momentum and Laplace-Runge-Lenz\nvector in the Kepler problem. Being referred to as the universal\nhamiltonian, universal angular momentum and universal\nLaplace-Runge-Lenz vector respectively, they are elements in\n(essentially) the TKK (Tits-Kantor-Koecher) algebra of V and\nsatisfy commutation relations similar to the ones for the\nhamiltonian, angular momentum and Laplace-Runge-Lenz vector in the\nKepler problem. We also give some examples of Poisson realization\nof the TKK algebra, along with the resulting classical generalized\nKepler problems. For the simplest simple euclidean Jordan algebra\n(i.e., mathbb R), we give examples of operator realization for\nthe TKK algebra, along with the resulting quantum generalized\nKepler problems.