Semiclassical approximations in infinitely connected spaces Zusammenfassung: The aim of this dissertation is to derive from first principles semiclassical approximations for quantum mechanical systems whose configuration space is infinitely connected. The emergence of such spaces is intimately related to magnetic forces which are classically inaccessible to the system under consideration but which nevertheless influence the latter’s quantum mechanical behavior. While a comprehensible analysis of the corresponding exact quantum mechanical solutions is often obstructed by their complicated form essential features of the dynamics collapse into discontinuities in Gutzwiller’s semiclassical propagator. The intention is thus to determine the origin of these discontinuities in anticipation of an accessible semiclassical picture.The first system under consideration is a charged particle propagating in the presence of an Aharonov Bohm magnetic flux line. The infinite connectedness of the problem arises as a consequence of the discontinuous dependence of Dirac’s magnetic phase factor on the number of windings of any closed curve encircling the flux. A novel semiclassical limit is introduced for the propagator of the otherwise free particle. While this limit directly produces the semiclassical approximation of Gutzwiller in backward propagation direction in forward direction it describes two half waves which acquire Dirac’s magnetic phase as if passing above and below the flux line respectively. This splitting of the wave mediates a smooth transition of the propagator’s phase from negative to positive values and gives rise to an interference pattern which is entirely determined by the contribution to Hamilton’s principal function associated with the angular motion of the particle with respect to the flux line. In a subsequent semiclassical limit in which Planck’s constant is neglected against any nonzero such angular contribution this smooth transition is no longer resolved and Gutzwiller’s expression is obtained also in forward propagationdirection where its phase is discontinuous.In order to describe further potentials besides the flux our thus obtained approximation is amended accordingly and iterated as in a path integral approach followed by an evaluation by the method of stationary phase. To this end the applicability of a method existing for this purpose for Cartesian problems is extended to accommodate for the first time also path integral expressions parametrized by generalized coordin ...