Path integration in conical space |
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Authors: | Akira InomataGeorg Junker |
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Affiliation: | a Department of Physics, State University of New York at Albany, 1400 Washington Avenue, Albany, NY 12222, USA b European Organization for Astronomical Research in the Southern Hemisphere, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany |
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Abstract: | Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. |
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Keywords: | Linear defects: dislocations, disclinations Cosmic strings Quantum mechanics: Path integral |
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