**Theory of self-adjoint operators and quantum fermionic systems with topological defects**

**Abstract:**

Topological defects appear as a consequence of spontaneous symmetry breaking in physical systems of various
spatial dimensions. The method of a self-adjoint extension of symmetric operators is employed to impose a boundary
condition for the quantized fermion field on the edge of the defect, and a general theory of quantum fermionic systems with
topological defects is developed. 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 graphytic monolayers
with disclinations.