Specialization: 010700/17 Theoretical and mathematical physics
Program: 28 Theory of elementary particles interaction and quantum field theory
Program supervisor: prof. M.A. Braun
Department of High  Energy Physics and Elementary Particles
Scientific adviser: prof. S.N. Manida
Reviewer: associate prof. M.I. Vyazovsky

Hamiltonian mechanics in the space of constant negative curvature.
V.P. Stepanov

Investigations of non-flat spaces are motivated by existence of non-nil cosmological term in Einstein equation. Hamiltonian formalism of the space of constant positive curvature (de Sitter space) have already been investigated. present work similar formalism and integrals of motion have been derived for the space of constant negative curvature (anti-de Sitter space).
At first calculations have been carried out in Beltrami coordinates, which could be identified with inertial frame coordinates. B free particle Hamiltonian in Beltrami coordinates appears to be time-dependent and does not coincide with free particle energy. In order to make them match new coordinates are introduced.
Because of radius of curvature of the space new term appears in Schroedinger equation, leading to new solution – linear oscillator.

The list of the publications
1. V.P. Stepanov. Hamiltonian mechanics in the spaces of constant negative curvature. // Conference abstracts International Student Conference “Science and Progress” DAAD St. Petersburg. 2011. p. 216.