Gorkavenko V. Quantum effects caused by external singular magnetic fields

Thesis is devoted to the investigation of the quantum effects caused by existence of the external singular magnetic field in the systems with quantized boson and fermion fields. In the case of the quantized boson field, the induced vacuum energy-momentum tensor was investigate in the arbitrary space-time dimension d + 1 in the presence of magnetic brane of the dimension d - 2, and the backreaction of the vacuum polarization effect on the background metric. In the case of the quantized fermion field at finite temperature at space-time dimension 2 + 1, the induced quantum numbers (fermion number, induced flux, spin, angular and total angular momentum) and its correlations are investigated. The analytical expressions were obtained for the components of the induced vacuum energy-momentum tensor of the quantized massive charged scalar field. Using semi-classical approach, it was found the first-order metric modifications and the corresponding gravitational potential and deficit angle. The analytical expressions were obtained for the induced quantum numbers of the ideal fermi-gas in the space-time dimension 2 + 1 at finite temperature in the presence of singular magnetic vortex. It was shown that the condition of the nonnegativeness of quadratic fluctuation imposes physical restrictions on the region of self-adjointness parameter, which labels boundary conditions at the location of the magnetic vortex