This volume provides a comprehensive review for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all co-ordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. In addition, the book provides an overview of some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, and their use in mathematical physics and quantum chaos. The volume also contains results on the study of the properties of a particular integrable billiard system in the hyperbolic plane, a proposal concerning interbasis expansions for spheroidal co-ordinate systems in four-dimensional Euclidean space, and some further results derived from the Selberg (super-) trace formula.
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