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The behaviour of a quantum particle in the spacetime region exterior to a circular cosmic string is studied by constructing a connection one-form in the tetrad formalism. In the weak-field approximation, near the string core, the space exhibits a conical singularity, with an attendant topological phase and distortion of the energy spectrum of a scalar particle determined by the global properties of the spacetime structure of the string loop.

Topological Effects of a Circular Cosmic String