Existence of the Dynamic Symmetries O_4 and SU_3 for All Classical Central Potential Problems
Abstract
It is found that all classical dynamic problems (relativistic as well as nonrelativistic) involving central potentials, inherently possess both O_4 and SU_3 symmetry. This leads to a generalization of both the RungeLenz 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 O_4 and SU_3 in terms of canonical variables is given. The question of a possible quantummechanical analog is discussed. Also, a constructive technique is given for imbedding the Lorentz group and SU_3 in an infinitedimensional Lie algebra.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 May 1967
 DOI:
 10.1143/PTP.37.798
 Bibcode:
 1967PThPh..37..798F