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On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane
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On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane
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In this paper I discuss by means of path integrals the quantum dynamics of a charged particle on the hyperbolic plane under the influence of an Aharonov-Bohm gauge field. The path integral can be solved in terms of an expansion of the homotopy classes of paths. I discuss the interference pattern of scattering by an Aharonov-Bohm gauge field in the flat space limit, yielding a characteristic oscillating behavior in terms of the field strength. In addition, the cases of the isotropic Higgs-oscillator and the Kepler-Coulomb potential on the hyperbolic plane are shortly sketched.
Forward citations
Cited by 2 Pith papers
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Morse Bridge between Planar Kepler and Hyperbolic Landau Dynamics
The radial Kepler problem and sectors of the hyperbolic Landau problem are mapped to the Morse spectral problem, relating their bound spectra, resonances, and scattering data.
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Planar Kepler and hyperbolic Landau dynamics both reduce to the Morse Hamiltonian, connecting Coulomb coupling to magnetic field times horocyclic momentum and Kepler shells to Morse threshold resonances.
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