Gell-Mann dynamic symmetry forN-level quantum systems

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Abstract
We present the concept of dynamic symmetry of the Gell-Mann type to the dynamical evolution of an arbitrary quantum system of N levels involving generally time-dependent interaction parameters which are of arbitrary strengths and which need not be precisely known. The most important consequence of the dynamic symmetry is the existence of a characteristic set of constants of motion which resembles the existence of a set of quantum numbers of various flavors in high-energy particle physics, and which implies various types of population trapping in the coherent excitation of atoms by lasers in intense-field electrodynamics.