Bound state in a model of electromagnetic field interacting with a material plan

Abstract

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

Neutrino Oscillations in the Model of Interaction of Spinor Fields with Zero-Range Potential Concentrated on a Plane

“…The DAF ( 5) is supposed to be used as the addition term to the action functional of renormalized models describing neutrino physics. The constructed model is an analog of the model of interaction of the QED fields with 2D matter, of which the investigation in the Gaussian approximation enabled one to obtain non-trivial theoretical results about Casimir and Casimir-Polder effects [23,24,27,31,42], scattering processes [32,40,41], and the bound state of photons and Dirac particles [37,39,43]. Within the Gaussian approximation of the proposed model, we consider the scattering of neutrinos on the material plane and analyze the influence of collisions with it on their oscillations.…”

“…It was applied to study the effects of interactions of quantum electrodynamics (QED) fields with two-dimensional materials [23,24]. Employing basic physical requirements of locality, renormalizability, and gauge invariance, which are assumed in this approach, we impose significant restrictions on the possible form of the model [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”