V. R. Khalilov

Fermion pair creation by a strong Coulomb field in 2+1 dimensions

The creation of charged fermion pairs by a strong external Coulomb field in a space with two dimensions is investigated. Exact solutions to the Dirac equation are found for the Coulomb external field in 2+1 dimensions. The equation for determining the critical charge is obtained and is numerically solved for a simplified model. The critical charge for 2+1 dimensions is much less than the critical charge for the similar model with 3+1 dimensions. The influence of the vacuum polarization on the critical charge is studied in the one-loop approximation to the (2+1)-dimensional quantum electrodynamics.

A (2+1)-dimensional fermion in the Coulomb and magnetic field backgrounds

In the problem of a two-dimensional hydrogen-like atom in a magnetic field background, we construct quasi-classical solutions and the energy spectrum of the Dirac equation in a strong Coulomb field and in a weak constant homogeneous magnetic field in 2+1 dimensions. We find some “exact” solutions of the Dirac and Pauli equations describing the “spinless” fermions in strong Coulomb fields and in homogeneous magnetic fields in 2+1 dimensions.

Polarization of vacuum by an external magnetic field in the (2 + 1)-dimensional quantum electrodynamics with a nonzero fermion density

The Greens function of the Dirac equation with an external stationary homogeneous magnetic field in the (2+1)-dimensional quantum electrodynamics (QED2+1) with a nonzero fermion density is constructed. An expression for the polarization operator in an external stationary homogenous magnetic field with a nonzero chemical potential is derived in the one-loopQED2+1 approximation. The contribution of the induced Chern—Simons term to the polarization operator and the effective Lagrangian for the fermion density corresponding to the occupation of n relativistic Landau levels in an external magnetic field are calculated. An expression of the induced Chern—Simons term in a magnetic field for the case of a finite temperature and a nonzero chemical potential is obtained.

QED2+1 radiation effects in a strong magnetic field

We develop the eigenfunction method for the Dirac operator in a background magnetic field in the (2+1)-dimensional quantum electrodynamics (QED2+1). In the eigenfunction repressentation, we find the exact solutions and the Greens functions of the Dirac equation in a strong constant homogeneous magnetic field in 2+1 dimensions. In the one-loop QED2+1 approximation, we derive the effective Lagrangian, the density of vacuum fermions induced by the field, and the electron mass operator in a homogeneous background magnetic field.

Nonlinear effects induced by vacuum polarization by a strong electromagnetic field in a weak static electromagnetic field

In the one-loop approximation of quantum electrodynamics, we study the Faraday rotation effect in the propagation of a weak linearly polarized wave through the field of a strong plane electromagnetic wave and also processes induced by a strong wave: the emission of a photon whose energy is an integer multiple of the “strong-wave quantum” and photon absorption with the emission of several photons identical (coherent) to the “strong-wave quanta.” The induced processes should occur in a vacuum in a superposition of external fields, namely, the field of a strong plane electromagnetic wave and a static spatially inhomogeneous electromagnetic field. We show that the induced photon emission in the field of a strong electromagnetic wave with circular polarization and in a static inhomogeneous field is equivalent to the merging of two “strong-wave quanta” with the production of one photon and that the induced photon absorption in the same combination of fields is equivalent to the decay (splitting) of a photon into two photons completely identical to the “strong-wave quanta.” All these effects are induced by the phenomenon of the vacuum polarization by a strong external time-dependent electromagnetic field. The probabilities of the induced processes are nontrivial nonlinear functions of the squared strength of the time-dependent field also depending on other parameters.

Neutral Fermion Having Electric and Magnetic Moments in an External Electromagnetic Field

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a “charged” fermion in a external field characterized by a certain “3-pseudo-vector potential.” The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.

Equilibrium of a degenerate gas of nucleons and electrons in a strong magnetic field

A model of a degenerate ideal gas of nucleons and electrons in a superstrong magnetic field is used to describe the state of matter in the central region of a strongly magnetized neutron star. The influence of a constant uniform superstrong magnetic field on the equilibrium conditions and the equation of state for the degenerate gas of neutrons, protons, and electrons is investigated in the framework of this model. The contribution determined by the interaction of the anomalous magnetic moments of the fermions with the magnetic field is taken into account. The influence of the superstrong magnetic field on the process of gravitational collapse of a magnetized neutron star is discussed under the assumption that the central region of the star consists mostly of degenerate neutrons. We show that if the densities of electrons, protons, and neutrons are relatively low depending on the field strength, the fermion gases in a superstrong uniform magnetic field become totally polarized with respect to the spin. We discuss the possibility of spontaneous magnetization occurring in a system of degenerate neutrons where the exchange interaction effects are taken into account.

Fermions in strong external fields in 2+1 and 1+1 dimensions

The creation of electron-positron pairs from a vacuum by an external Coulomb field is examined within (2+1)-dimensional quantum electrodynamics. If the electromagnetic coupling constant exceeds 0.62 (Z= 85), then in a simple model with a finite-size nucleus, the lower electron level crosses the boundary of the negative-energy continuum (i.e., Dirac sea), and a hole (i.e., positively charged fermion) appears in the negative-energy continuum. An equation is obtained that describes the levels of the ground and excited electron states in a strong Coulomb field of the nucleus. The critical nucleus charge is found for a few lowest electron states. The critical charge in 2+1 dimensions is significantly smaller than in 3+1 dimensions. The problem is reduced to the case of a bounded Coulomb field in 1+1 dimensions without a magnetic field. The interaction of a fermion and an external scalar field in 2+1 and 1+1 dimensions is investigated.

Induced vacuum charge of massless fermions in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions

We study the vacuum polarization of zero-mass charged fermions in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions. For this, we construct the Green’s function of the two-dimensional Dirac equation in the considered field configuration and use it to find the density of the induced vacuum charge in so-called subcritical and supercritical regions. The Green’s function is represented in regular and singular (in the source) solutions of the Dirac radial equation for a charged fermion in Coulomb and Aharonov–Bohm potentials in 2+1 dimensions and satisfies self-adjoint boundary conditions at the source. In the supercritical region, the Green’s function has a discontinuity related to the presence of singularities on the nonphysical sheet of the complex plane of “energy,” which are caused by the appearance of an infinite number of quasistationary states with negative energies. Ultimately, this situation represents the neutral vacuum instability. On the boundary of the supercritical region, the induced vacuum charge is independent of the self-adjoint extension. We hope that the obtained results will contribute to a better understanding of important problems in quantum electrodynamics and will also be applicable to the problem of screening the Coulomb impurity due to vacuum polarization in graphene with the effects associated with taking the electron spin into account.

Quantum Macroscopic Effects in a Degenerate Strongly Magnetized Nucleon Gas

A model of a degenerate gas consisting of neutrons that are in chemical equilibrium with degenerate protons and electrons in a stationary and homogeneous superstrong magnetic field is used to describe the state of the matter in central regions of strongly magnetized neutron stars. Expressions for thermodynamic quantities (such as energy density, particle density, pressure, and magnetization) characterizing a degenerate gas of neutrons, protons, and electrons are obtained. In these expressions, the contributions determined by the interaction between anomalous magnetic moments of fermions and the magnetic field are taken into account. Macroscopic effects that may occur in strongly magnetized neutron stars are discussed. We show that all thermodynamic quantities characterizing electrically charged fermions in a strong magnetic field are subject to nonperiodic oscillations caused by the interaction of the anomalous magnetic moments of protons and electrons with the magnetic field. We also show that if the nucleon density and the electron density exceed threshold values that are relatively small and depend on the magnetic field strength, all fermions are fully polarized with respect to the spin. The full spin polarization effect in neutrons is caused by the interaction between the anomalous magnetic moment and the magnetic field. The obtained results may prove useful in understanding processes that occur in the nucleus of a neutron star with a magnetic field “frozen into” the star.