Non-perturbative Euler-Heisenberg Lagrangian and Paraelectricity in Magnetized Massless QED

In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta much smaller than $\sqrt{eH}$, the magnetic field introduces a dynamical ultraviolet cutoff in the theory that also enters in the non-perturbative Euler-Heisenberg action. Using this action, we show that the system exhibits a significant paraelectricity in the direction parallel to the magnetic field. The nonperturbative nature of this effect is reflected in the non-analytic dependence of the obtained electric susceptibility on the fine-structure constant. The strong paraelectricity in the field direction is linked to the orientation of the electric dipole moments of the pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.Comment: 18 pages, to be published in NP

Magnetoelectric Effect in Strongly Magnetized Color Superconductivity

The effect of a strong magnetic field on the electric polarization of a three-flavor color superconducting medium is investigated. We found that the electric susceptibility of this strongly magnetized medium is highly anisotropic. In the direction transverse to the applied magnetic field the susceptibility reduces to that of the vacuum, while in the longitudinal direction it depends on the magnetic field and decreases with it. The nature of this behavior is associated with the field's dependence of the Cooper pairs' coherence length, which plays the role of the electric dipole length. The field's dependence of the electric polarization is interpreted as the realization of the magnetoelectric effect in cold-dense quark matter.Comment: 10 pages, 1 figur

Electromagnetic radiation security estimation on the residential building roof for cellular antenna

The work objective is to estimate the electromagnetic environment on the roof where a mobile system base station aerial is installed. The problem arises during maintenance, repair, and assembly operations for antenna-feeder devices. The evaluation problem for ecological assessment of the electromagnetic environment at a standard height of two meters above the roof is solved with the computational prediction method. Two strict models are used for electrodynamic simulation of energy flux density, i.e. a two ray model which describes the plane electromagnetic wave diffraction on the flat perfectly conducting roof surface, and finite models of the roof are described with the canonical problem on a wedge of infinite extent. The difference between the developed model and the known ones lies within the research possibility not only in the computational points but within a whole computational plane. In the simulation process, antenna emission characteristics can be set in a number of ways including those obtained from the radiation object specifications, as it is proposed in a well-known technique. The simulation results for energy flux density distribution in a horizontal plane within the roof space are given. Computational points are placed at the square grid nodes with the period of a quarter wavelength of the transmitter. A physical interpretation of the obtained results is given. A safety conclusion on the human presence on the roof with operating directional cel lular antenna of GSM standard is formulated