Self-adjointness and bounded systems in quantum theory

Lecture by Prof. Yurii Sitenko (National Academy of Sciences Ukraine, Kiev)

August 3, 2022, 3:30 p.m.

Abstract:
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 quantum
matter 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.

ESI Boltzmann Lecture Hall