SEMICLASSICAL TRACE FORMULAS FOR SYSTEMS WITH NON-ABELIAN SYMMETRY

We derive generalizations of the trace formula of Gutzwiller and Balian and Bloch that are valid in the presence of a non-Abelian continuous symmetry. The usual trace formula must be modified in such cases because periodic orbits occur in continuous families, whereas the usual trace formula requires that the periodic orbits be isolated at a given energy. These calculations extend the results of a previous paper, in which we considered Abelian continuous symmetries. The most important application of the results of this paper is to systems with full three-dimensional rotational symmetry, and we give this case special consideration.