On the Path Integral in Imaginary Lobachevsky Space

TL;DR

This paper evaluates the path integral in imaginary Lobachevsky space, addressing the Kepler problem and magnetic fields, providing insights into quantum mechanics in hyperbolic geometries.

Contribution

It presents a novel evaluation of the path integral in hyperbolic space and discusses specific physical problems within this geometric framework.

Findings

Path integral in imaginary Lobachevsky space is explicitly computed.

Analysis of the Kepler problem in hyperbolic geometry.

Discussion of quantum effects under constant magnetic fields.

Abstract

The path integral on the single-sheeted hyperboloid, i.e.\ in $D$-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call ``Kepler-problem'', and the case of a constant magnetic field are also discussed.