Bound states in a model of interaction of Dirac field with material plane

Abstract

Abstract. In the framework of the Symanzik approach model of the interaction of the Dirac spinor field with the material plane in the 3 + 1-dimensional space is constructed. The model contains eight real parameters characterizing the properties of the material plane. The general solution of the Euler-Lagrange equations of the model and dispersion equations for bound states are analyzed. It is shown that there is a choice of parameters of the model in which the connected states are characterized by dispersion law of a massless particle moving along the material plane with the dimensionless Fermi velocity not exceeding one.

Dispersion relations and dynamic characteristics of bound states in the model of a Dirac field interacting with a material plane

“…The Casimir force can be both attractive and repulsive [4]. The characteristics of photons and Dirac particles scattering on the defect plane can be calculated in the model, also the properties of states localized near the defect plane can be investigated [6][7][8][9][10][11].…”

“…It was developed for the description of interaction of the fields of quantum electrodynamics (QED) with extended material objects [4]. Such an approach makes it possible to describe quantitatively many physical phenomena within the framework of one universal model with a small number of parameters [4][5][6][7][8][9][10][11]. In the present paper we formulate general principles that have been used to construct models for the interaction of QED fields with two-dimensional material objects within the framework of the Symanzik approach and present the latest results obtained by us…”

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

“…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].…”