Symanzik approach in modeling of bound states of Dirac particle in singular background

Abstract

Abstract. In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are studied. For localized near plane Dirac particle the expression for current, charge and density are presented. For bound state with massless dispersion law the current, charge and density are calculated for simplified model with 2 parameter exactly.The model can find application to a wide class of phenomena arising by the interaction of fields of quantum electrodynamics with two-dimensional materials.Investigation of macroscopic quantum phenomena is an important direction in experimental and theoretical physics which has attracted recently the attention of many researchers. In this area, the main problem of modelling employing the principles of quantum field theory is that the space-time homogeneity and isotropy, which is typical for usual quantum field theory models of elementary particles [1], must be broken. The symmetry properties of the vacuum may change essentially as a result of interactions of quantum fields with macroscopic objects. Therefore quantum macro effects may appear in dynamics of material bodies which cannot be explained both in classical physics and in framework of non relativistic quantum mechanics.Theoretically, this problem was first considered in 1948 by Casimir [2]. He showed that the fluctuations of the quantum vacuum generate attraction between ideally conducting plates of a planar uncharged capacitor. This phenomenon, called the Casimir effect (CE), is observed experimentally [3][4][5][6], and the empirical results obtained for materials with high conductivity, with a high degree of accuracy, are in agreement with theoretical ones.At typical for CE distances of 10 to 1000 nm both classical and quantum properties of the system turn out to be essential. Their combination forms a special nanophysics. Investigation of it is not solely of theoretical interest, understanding its particular feature is also important for developing new technological devices, in view of the increasing trend to their miniaturization.Although theoretical investigations of the CE are the subject of numerous works [6,7], they are often based on simplified models ignoring usually specificity of quantum electrodynamics. Such models are not suitable for comprehensively describing a wide range of nanophysical phenomena occurring in a system as a result of the interaction of its quantum degrees of freedom with material bodies of a given shape (classic defect).In our work we used the the Symanzik's approach [8], modelling the interaction of quantized fields with a spatial inhomogeneity with the aid of an additional action functional (defect action), concentrated in the spatial domain where this inhomogeneity -a macroscopic object -is located. It is

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].…”