Anomalous Magnetic Moment of an Electron in a Static Magnetic Field in the Topologically Massive 2D Electrodynamics
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Anomalous Magnetic Moment of an Electron in a Static Magnetic Field in the Topologically Massive 2D Electrodynamics P. A. Eminov National Research University Higher School of Economics, Moscow, 101000 Russia e-mail: [email protected] Received October 26, 2019; revised November 26, 2019; accepted November 27, 2019
Abstract—An analytic equation for the anomalous magnetic moment of an electron in a static magnetic field in the topologically massive 2D electrodynamics is obtained in the single-loop approximation. The asymptotic expressions describing the dependence of the anomalous magnetic moment on the dimensionless Chern–Simons parameter and the dynamic field parameter are determined in the limiting case of a relatively weak magnetic field. The applicability conditions for the results of calculations of the anomalous electron magnetic moment based on the evaluation of the vertex function in the 2D electrodynamics with the Chern– Simons term are established. DOI: 10.1134/S1063776120040068
1. INTRODUCTION Analysis of quantum processes of the (2 + 1)dimensional space–time attracts considerable attention due to practical applications in the physics of condensed state of matter [1–3] and peculiar properties of topologically massive 2D models in the quantum field theory [4, 5]. Further investigations of radiative and spin effects in the (2 + 1)-dimensional quantum electrodynamics (QED2+1) with initial conditions such as an external field, finite temperature, and density of a substance are topical. The first results of analysis of anomalous magnetic moment (AMM) of an electron in the topologically massive QED2+1 with the Chern–Simons term were obtained based of the calculation of the vertex function disregarding the effect of an external magnetic field [6–10]; in [10], the case of a nonzero temperature was also considered. In [11], for analyzing the experimental results obtained in [12, 13], the electron AMM was calculated based on the pseudo-QED2+1 in the approximation linear in the field (i.e., disregarding the dynamic nature of the electron AMM) [14–19]. It should be noted that in publications [20–22] devoted to analysis of the electron AMM in the P-even 2D model of quantum electrodynamics, the spectral representation of the photon propagator was used for eliminating the infrared divergence of the vertex function in a static magnetic field. The radiation energy shift of the electron ground state in a static magnetic field was calculated in [23] and [24] using 2D electrodynamics with the Chern–Simons term and without it, respectively.
Comprehensive description of the electron stationary states in a static magnetic field was given in [25] taking into account the spin properties in the QED2+1 model with the double fermion representation [26, 27]. This result was used in [25] for calculating the radiation energy shift of the electron ground state in a magnetized plasma in the topologically massive 2D electrodynamics as well as the electron AMM in a comparatively weak magnetic field. The AMM of excit
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