Creation of Spin-1/2 Particles in the Hyperboloid de Sitter Space-Time

In this work we solve Dirac equation by using the method of seperation of variables. Then we analyzed the particle creation process. To compute the density number of particles created Bogoliubov transformation technique is used.Comment: 5 pages, no figures, presented at the 1st Int. Hellenic&Turkish Phys. Con

Coulomb Green’s Function in Lobachevsky Space

The Green’s function of the Schr¨odinger equation with the Coulomb potential in the space of constant negative curvature is constructed in the form of an eigenfunction expansion. The closed form expression for this function is also presented

Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page