Remarks on dynamical and noncompact groups in physics and chemistry

Abstract

In contrast to the usual degeneracy or symmetry groups, the new dynamical groups generate all the energy levels and spectrum of a system in one infinite-dimensional representation. The origin and nature of these groups as they came up first in high-energy physics, then in atomic physics, are outlined. The known dynamical groups, e.g., for the rigid rotor, the harmonic oscillator, and the hydrogen atom, are displayed. Possible applications in molecular spectroscopy are discussed.