Spectrum generating algebras for the classical Kepler problem

Abstract

It is shown that the so(4, 2) spectrum generating algebra for the classical Kepler problem for non-zero energies can be obtained from the generators of the spacetime conformal group SO(4, 2). This is achieved by exploiting the equivalence of Kepler motion and null geodesic motion in conformally flat Einstein static spacetimes. We show that it is the existence of a time-dependent representation of the so(4, 2) spectrum generating algebra for null geodesic motion in the Einstein static spacetimes (originating from the so(4, 2) algebra of first integrals) which determines the corresponding spectrum generating algebra structure in the classical Kepler problem. Further, for the zero energy state, it is shown that only the iso(3) invariance subalgebra has a direct physical significance.