Modelling of Bound States of Dirac Particles in Singular Background in Framework of Symanzik Approach

The problem of interaction of the fields of quantum electrodynamic with material macro-object is considered by employing the Symanzik approach on modelling the interaction of quantum field with space-time inhomogeneities. Results obtained in the models with Chern–Simons interaction of photon field with 2-dimensional material are briefly reviewed. In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are considered. For localized near plane Dirac particle the dispersion relation and the expressions for current, charge and density are analyzed. The bound states with massless dispersion law is considered. The presented methods of modelling can find application to a wide class of phenomena emerging from the interaction of quantum fields with extended material structures.