Topological phenomena are of great interest and importance because of their universal nature connected with general properties of space-time, as well as of their numerous practical applications. Since the discovery of Aharonov and Bohm in 1959, it has become clear that topology has to do with the fundamental principles of quantum theory. At present much attention is paid to the study of nonperturbative effects in quantum systems, arising as a consequence of interaction of quantized fields with various configurations of classical fields. Especial interest is to the investigation of the influence of configurations with nontrivial topology (kinks, vortices, monopoles, or, in general, topological defects) on the properties of quantum systems. There is a need, in this regard, to take account of the finite size of a topological defect and to set up a boundary condition on its edge. Our idea consists in the employment of the most general boundary conditions ensuring the impenetrability of quantized fields into the interior of a topological defect; in mathematical parlance, this means the condition of self-adjointness for the appropriate quantum-mechanical operator of energy. We set the task of discovering effects which are induced by a topological defect in general case in the ground state of quantum matter system.

Further analysis and the requirement of physical plausibility of obtained results may restrict the ambiguity in the choice of boundary conditions. In this case, there is an opportunity of the unambiguous determination of effects which are induced by a topological defect in quantum matter, see [1,2]. In the present project a topological defect in the form of the Abrikosov-Nielsen-Olesen vortex is considered. Such defects are known in cosmology and astrophysics under the name of cosmic strings, they emerge in the aftermath of phase transitions with spontaneous gauge symmetry breaking during evolution of the early Universe. The vortex-type defects are widely discussed in the context of condensed matter physics as well, in particular, they can be viewed as disclinations in graphene-like structures, see [3]. I plan to study the influence of the vortex-type defect on the surrounding quantum bosonic matter. Quantum numbers which are induced in the ground state by the vortex-type defect will be determined, and their dependence on the gauge flux and string tension, as well as on the size of the defect and choice of boundary conditions, will be analyzed.

1. Yu.A. Sitenko. Induced vacuum magnetic field in the cosmic string background, Phys. Rev. D 104 (4), 045013 (2021).

2. Yu.A. Sitenko, V.M. Gorkavenko, Induced vacuum magnetic flux in quantum spinor matter in the background of a topological defect in two-dimensional space, Phys. Rev. D 100 (8), 085011 (2019).

3. Yu.A. Sitenko, N.D.Vlasii. Electronic properties of graphene with a topological defect, Nucl. Phys. B 787 (3), 241-259 (2007).