1967/05/01 by D. M. Fradkin · 125 citations
Physics and Astronomy · Mathematics · #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #Astro and Planetary Science #Physics #Kepler problem #Harmonic oscillator #Homogeneous space #Lorentz transformation #Lie group #Generalization #Symmetry (geometry) #Mathematical physics #Lie algebra #Tensor (intrinsic definition) #Symmetry group #Constructive #Algebra over a field #Classical mechanics #Quantum mechanics #Pure mathematics #Mathematical analysis #Mathematics
paper · pdf · doi:10.1143/ptp.37.798
published in Progress of Theoretical Physics 37(5), 798-812 (Oxford University Press)
openalex publication_date 1967/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
It is found that all classical dynamic problems (relativistic as well as non-relativistic) involving central potentials, inherently possess both O4 and SU3 symmetry. This leads to a generalization of both the Runge-Lenz vector in the Kepler problem and the conserved symmetric tensor in the harmonic oscillator problem. For a general central potential, an explicit construction of the elements of the Lie algebra of O4 and SU3 in terms of canonical variables is given. The question of a possible quantum-mechanical analog is discussed. Also, a constructive technique is given for imbedding the Lorentz group and SU3 in an infinite-dimensional Lie algebra.