Path integration on the hyperbolic plane with a magnetic field
The author discusses the path integrals on three formulations of hyperbolic geometry, where a constant magnetic field B is included. These are: the pseudo-sphere, the Poincaré disc, and the hyperbolic strip. The corresponding path integrals can be reformulated in terms of the path integral for the modified Pöschl-Teller potential. The wave-functions and the energy spectrum for the discrete and continuous part of the spectrum are explicitly calculated in each case. First the results are compared for the limit \(B\to 0\) with previous calculations and second with the path integration on the Poincaré upper half-plane.
scientific article; zbMATH DE number 4194750
scientific article