Motion of neutral fermions with anomalous magnetic and electric moments in external fields

A covariant spin operator is found for fermions with anomalous magnetic and electric dipole moments in constant external fields. The spin behavior of a neutral fermion in constant magnetic and electric fields is investigated using exact solutions obtained for the Dirac equation.     

Pair Production and Solutions of Wave Equation for Arbitrary-Spin Particles

We investigate the theory of particles with arbitrary spin and magnetic moment in the Lorentz representation (0, s) (s, 0) in an external constant and uniform electromagnetic field. We obtain the density matrix of free particles in pure spin states. The differential probability of pair producing particles with arbitrary spin by an external constant and uniform electromagnetic field is found using the exact solutions. We calculate the imaginary and real parts of the Lagrangian in an electromagnetic field that takes into account the vacuum polarization.     

Extended Lagrangian formalisms for dyons and some applications to solid systems under external fields

We analyze the conditions of the electromagnetic potentials for systems with electric and magnetic charges and the Lagrangian theory with these potentials. The constructed Lagrangian function is valid for obtaining the field equations and the extended Lorentz force for dyonic charges for both relativistic particles in vacuum and non-relativistic entities in solids. In a second part, with the one-body Hamiltonian of independent particles in external fields, we explore some dual properties of the dyonic system under external fields. We analyze the possible diamagnetic (and ‘diaelectric’) response of magnetic monopoles under a weak and constant electromagnetic field and the theory of Landau levels in the case of magnetic charges under strong electromagnetic constant fields.     

A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

Polarization of an electron-positron vacuum by a strong magnetic field with an allowance made for the anomalous magnetic moments of particles

Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculated Lagrangian matches the standard Heisenberg-Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears and the Lagrangian tends to a constant determined by the anomalous magnetic moments of the particles.     

Charged particle motion in an electromagnetic field on Kerr background geometry

In this paper we study the trajectories of charged particles in an electromagnetic field superimposed on the Kerr background. The electromagnetic fields considered are of two types: (i) a dipole magnetic field with an associated quadrupole electric field, (ii) a uniform magnetic field. The contribution of the background geometry to the electromagnetic field is taken through the solutions of Petterson and Wald respectively. The effective potential is studied in detail for ther-motion of the particles in the equatorial plane and the orbits are obtained. The most interesting aspect of the study is the illustration of the effect of inertial frame dragging due to the rotation of the central star. This appears through the existence of nongyrating bound orbits at and inside the ergo surface. The presence of the magnetic field seems to increase the range of stable orbits, as was found in a previous study involving the Schwarzschild background.     

Motion of a particle in a static magnetic field and in the field of a electromagnetic plane wave

The solutions of the equations of motion of a charged particle in an external electromagnetic field consisting of a superposition of a constant uniform magnetic field and the field of a circularly polarized electromagnetic plane wave are presented as solutions of the Cauchy problem. The resonance case is studied. Zh. Tekh. Fiz. 67, 94–99 (February 1997)     

Liouville and Fokker–Planck dynamics for classical plasmas and radiation

We consider a nonequilibrium statistical system formed by many classical non‐relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase‐space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF f_in. The CPSPDF f and f_in, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and f_in imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), f_in describes local equilibrium but global nonequilibrium, and we propose a long‐time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t ≤ 0, is subject to weak external charge‐current distributions: then, new hierarchies for moments and their long‐time behaviours are discussed in outline. As examples, approximate mean‐field (Vlasov) approximations are treated for both cases 1) and 2).     

Orthonormal tetrads and the charged fluid in general relativity

A space-time filled with the self-gravitating charged fluid with constant electric permitivity and constant magnetic permeability is investigated. On expressing the stress-energy tensor in terms of an orthonormal tetrad, the equations of motion and Maxwell equations are formulated. In case of the geodesic flow, the conditions for divergence-free electric and magnetic fields are obtained. It is shown that the space-time permeated by the charged fluid with the electric field orthogonal to the magnetic one is embedded in 5-dimensional flat class-one space-time if and only if the electromagnetic energy flux vector vanishes.     

Motion of electron with anomalous moments in parallel electric and magnetic fields

An accurate solution is obtained for the Dirac equation describing the motion of an electron with anomalous moments in constant, homogeneous, and parallel electric and magnetic fields. The system of solutions obtained is shown to be orthogonal and complete with respect to the scalar product defined in the null plane X^oX³=const. The solutions obtained pass smoothly in the limit to steadystate solutions describing the motion of an electron with anomalous moments in a homogeneous magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–28, January, 1978.It remains to thank V. G. Bagrov for useful discussions of the work.     

Asymptotic analysis of ultra-relativistic charge

This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.     

Scattering lengths and baryon magnetic moments in a gauge model of strong and electromagnetic interactions

We present a broken SU(3) gauge model of strong and electromagnetic interactions with the usual vector mesons. All particles (9 vectors, 8 baryons and 9 pseudoscalars) have the right masses by means of the Higgs mechanism. We study the consequences of Sakuraï's idea that strong and electromagnetic interactions are mediated by vector mesons universally coupled to nearly conserved currents: one finds encouraging values for scattering lengths except for P-wave parameters in the meson-baryon sector that are too small. The calculation of the baryon anomalous magnetic moments also gives too-small numbers.     

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparameterization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are derived. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.     

Modified Nonlinear Model of Arcsin-Electrodynamics

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.     

非相对论下均匀斜交电磁场中正电荷的运动状况分析

文章对非相对论下均匀斜交电磁场中的正电荷+q进行了动力学矢量分析,将其运动分解为沿磁场方向的匀加速直线运动、垂直于电、磁场方向的匀速直线运动和垂直于磁场方向的匀速率圆周运动,进而推理出电荷完整的运动学方程;然后将运动学方程进行“约化”和简化,作出不同初速度下电荷在xy平面内的投影运动轨迹并加以分析,指出轨迹的若干特点及其内在的原因;举例作出电荷的空间轨迹图并指出其中蕴含的共性;对均匀正交电磁场情形下的3种特殊情况进行了讨论.此外,文末还指出本文解法的核心思想是参考系的切换.     

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.     

Radiation of de-excited electrons at large times in a strong electromagnetic plane wave

The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.