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.

Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry

“…From now on, in order to obtain analytical solutions, we will use the biharmonic coordinate system (BC), in which b = r, to describe a particular kind of hyperboloid [30], here called polar hyperboloid. In this case, the metric element simplifies to:…”

Quantum Theory of Multi-Local Particle

“…The theory of pseudo-spherical functions on non-compact space ) (Limi'c et al, 1967 (Strichartz, 1973) shows variety of series of eigenvalues, including continuous as well as discrete ones. An explicit form of the eigenfunctions are recently obtained for D = 3 (Kowalski et al, 2011). The real eigenvalues of single valued eigenfunctions on the non-compact base space are of the same form as those of the compact space except some supplementary continuous series.…”

On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

“…system was recently used to develop the pseudospherical functions on an one-sheeted polar hyperboloid [31]. These functions may be important if we consider problems where the solution of the Laplace equation in systems with hyperbolic symmetry is demanded.…”