Finite-Dimensional Spectrum-Generating Algebras

Abstract

It is suggested that the generators of a spectrum-generating algebra are all constants of the motion, some of them having an explicit time dependence. Also suggested is a specific form of the Hamiltonian action on the spectrum-generating algebra for systems with a finite number of degrees of freedom. Well-known examples of spectrum-generating algebras are shown to fit into this framework. The stability of the suggested structure against small perturbation is discussed. The question of the generalization of the suggested structure to systems with an infinite number of degrees of freedom is briefly commented upon.