On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane

Details On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane

1998-08-27

arxiv.org/abs/quant-ph/9808060v1

Int.J.Theor.Phys. 38 (1999) 955-969

Physics

Quantum Physics

LaTeX 12 pp., one figure

Scientific paper

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.

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