Theory of relativistic quantum fermionic systems with topological defects

Topological phenomena are of great interest and importance because of their universal nature connected with general properties of space-time, on the one hand, and their numerous practical aspects, on the other hand. We carry out a comprehensive and self-consistent study of the influence of topological defects on the properties of relativistic quantum fermionic systems. The method of a self-adjoint extension of symmetric operators is employed to impose a physically acceptable boundary condition for the quantized fermion field at the edge of the defect, and a general theory is elaborated. The theory explains unusual quantum numbers which are induced in the Dirac monopole background at CP violation. The theory predicts the emergence of charge and other quantum numbers in carbon monolayers (graphene) with disclinations. We determine the local density of one-particle states in such systems.