Quantum Theory on Lobatchevski Spaces

Understand

In this paper we set up a general formalism to deal with quantum theories on a Lobatchevski space, i.e.

• a spatial manifold that is homogeneous, isotropic and has negative curvature.
• The heart of our approach is the construction of a suitable basis of plane waves which are eigenfunctions of the Laplace-Beltrami operator relative to the geometry of the curved space.
• These functions were previously introduced in the mathematical literature in the context of group theory; here we revisit and adapt the formalism in a way specific for quantum mechanics.