Pseudospherical functions on a hyperboloid of one sheet

Abstract

The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra. The pseudospherical functions with half-integer order are investigated. The counterparts of the Legendre functions for the hyperboloid are introduced and a new class of pseudospherical functions is found.

References in corpus (3)

• Coherent state quantization of a particle in de Sitter space
• Quantization and spacetime topology
• Quantum particle on hyperboloid

Cited by in corpus (3)

• On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry
• Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry
• Topological spin excitations induced by an external magnetic field coupled to a surface with rotational symmetry