Wave Packets of Bound States of a Dirac Field on a Material Plane

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].…”

“…The interaction of photon fields with a two-dimensional (2D) object is carried out by the Chern-Simons potential, including only one dimensionless parameter and concentrated on a 2D-subspace of full Minkowski space-time [23,24,[27][28][29][30][31][32]. To describe the interaction of homogeneous and isotropic material plane with spinor field, one needs, in the most general case, no more than eight dimensionless constants [33][34][35][36][37][38][39]. Within the framework of models constructed in this way, a number of unusual effects have been found.…”

“…In particular, it is shown that the Casimir force between thin plates of an uncharged capacitor can not only be attractive, but also repulsive [23,24]. Using the Symanzik approach, we constructed models of interaction of Dirac particles with 2D materials, studied their bound states, scattering on a material plane [33][34][35][36][37][38][39][40][41], and calculated the Casimir force generated by vacuum fluctuations of quantum massless Dirac fields between two parallel thin plates [42].…”

Zero-range potential in the model of the spinor field interacting with a material plane: conditions for transparency of the plane to Dirac particles

“…They were used, in particular, in the models of interaction of fields of quantum electrodynamics [2] (QED) with two-dimensional (2D) material objects constructed within the framework of the Symanzik approach [3][4][5][6][7][8][9][10][11] . In these models, the Casimir forces and the characteristics of the processes of scattering of photons and Dirac particles were calculated, and the properties of bound states were also studied [3][4][5][6][7][8][9][10][11]. The aim of our work is to investigate the possibilities of special processes in the interaction of Dirac particles with a 2D-material in which their dynamics do not differ from the dynamics of free particles and in this sense the material object turns out to be transparent.…”