Path Integration on Hermitian Hyperbolic Space

Abstract

In this paper the path integral technique is applied to the quantum motion on the Hermitian hyperbolic space HH(2). The Schrödinger equation on this space separates in 12 coordinate systems which are closely related to the coordinate systems on the two-dimensional hyperboloid. For six coordinate systems out of the twelve it is possible to find a path integral solution.

29 pages, revised paper as published

References in corpus (5)

• Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space
• Superintegrability on the two dimensional hyperboloid II
• The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid
• On the Path Integral in Imaginary Lobachevsky Space
• Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

Cited by in corpus (1)

• Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: I. Darboux Spaces DI and DII