Spectral asymptotics on stationary space-times

We review our recent relativistic generalization of the Gutzwiller–Duistermaat–Guillemin trace formula and Weyl law on globally hyperbolic stationary space-times with compact Cauchy hypersurfaces. We also discuss anticipated generalizations to non-compact Cauchy hypersurface cases.

Sensitivity of elastic electron scattering off the 3He to the nucleon form factors

Elastic electron-3He scattering is studied in the relativistic impulse approximation. The amplitudes for the three-nucleon system – 3He – are obtained by solving the relativistic generalization of the Faddeev equation. The charge and magnetic form factor are calculated and compared with the experimental data for the momentum transfer squared up to 100 fm-2. The influence of the various nucleon form factors is investigated.

Relativistic path integral Monte Carlo: Relativistic oscillator problem

Relativistic generalization of path integral Monte Carlo (PIMC) method has been proposed. The problem of relativistic oscillator has been studied in the framework of this approach. Ultra-relativistic and nonrelativistic limits have been discussed. We show that PIMC method can be effectively used for investigation of relativistic systems.