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The motion of a particle in the field of dispiration (due to a wedgedisclination and a screw dislocation) is studied by path integration. Bygauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, andtorsion of the medium of dispiration. Then we carry out explicitly pathintegration for the propagator of a particle moving in the non-Euclidean mediumunder the influence of a scalar potential and a vector potential. We obtainalso the winding number representation of the propagator by taking thenon-trivial topological structure of the medium into account. We extract theenergy spectrum and the eigenfunctions from the propagator. Finally we makesome remarks for special cases. Particularly, paying attention to thedifference between the result of the path integration and the solution ofSchr\"odinger's equation in the case of disclination, we suggest thatSchr\"odinger equation may have to be modified by a curvature term.

Path integration in the field of a topological defect: the case of dispiration