Rectilinear motion of a charged magneton in electromagnetic fields

Uniform and rectilinear motion of a classical spin particle, a charged magneton, is considered in external electromagnetic fields of special type. The equations of motion are solved in both the vector and tensor methods of describing the spin. The rectilinear motion of a hyperbolically accelerated magneton is also considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 62–65, April, 1980.It is a pleasant duty to thank Professor V. G. Bagrov for suggesting the problem and discussing the results of the paper.     

Equations of motion of a spinning relativistic particle in external fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations. Zh. éksp. Teor. Fiz. 113, 1537–1557 (May 1998)     

Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment

The Lagrangian and Hamiltonian formulations for the relativistic classical dynamics of a charged particle with dipole moment in the presence of an electromagnetic field are given. The differential conservation laws for the energy-momentum and angular momentum tensors of a field and particle are discussed. The Poisson brackets for basic dynamic variables, which form a closed algebra, are found. These Poisson brackets enable us to perform the canonical quantization of the Hamiltonian equations that leads to the Dirac wave equation in the case of spin 1/2. It is also shown that the classical limit of the squared Dirac equation results in equations of motion for a charged particle with dipole moment obtained from the Lagrangian formulation. The inclusion of gravitational field and non-Abelian gauge fields into the proposed formalism is discussed.Received: 4 June 2005, Published online: 27 July 2005     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

On the Poincaré-invariant equations for particles with variable spin and mass

The Poincaré-invariant equations without redundant components, describing the motion of a particle which can be in different spin and mass states are obtained. The quasi-relativistic equation for a particle with arbitrary spin in external electromagnetic field is found. The group-theoretical analysis of these equations in carried out.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.     

On a generalization of the equations of electrodynamics

Both the field equations and the equations of motion of a charged particle in an electromagnetic field are generalized. The sense of the generalization consists in giving up the Lorentz condition on the field potentials. The basic conclusion is that, in addition to the charge and mass, the proper rotation of the particle (the spin) should belong to the characteristics of a particle in classical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 107–110, July, 1972.The author wishes to thank the participants of the Ivanov Inter-Institute Seminar on Mathematical and Theoretical Physics for discussion of the results of the present work.     

Classical spin theory

Tensor and vector equations of motion of a classical charged particle with spin have been derived within the framework of the special theory of relativity on the basis of Frenkel's tensor. The anomalous magnetic moment of the particle is considered in a natural manner in deriving the equations. The expression for the forces acting on the particle is constructed with consideration of the effect of spin on the motion trajectory. The spin equations proved to coincide with those obtained previously by Nyborg and Good. The properties of these equations have been studied, and it has been shown that the various equations are in fact variant forms of one and the same equation. In the absence of an anomalous magnetic moment the tensor equation coincides with Frenkel's spin equation, and in the same situation the vector equation transforms to the equation obtained by Tamm. In the special case of homogeneous fields the vector equation coincides with the well-known Bargmann-Michel-Telegdi equation. In conclusion we present spin motion equations for a particle with electric and magnetic charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–76, February, 1980.     

也谈带电粒子在电磁场中动态受力平衡条件

电磁场中相对论带电粒子的经典轨道运动受到洛伦兹力和辐射阻尼力的影响,在一定条件下会达到受力平衡状态．基于洛伦兹一狄拉克方程,本文介绍了计及辐射阻尼力后电磁场中带电单粒子(包括导体中的自由电子)受力平衡条件的一种可能的相对论协变形式．     

Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

Zur Theorie der Teilchenbewegung in zeitabhängigen elektromagnetischen Feldern

The Langevin equation – i.e. the equation of motion for a charged particle including a collision term proportional to the particle velocity – is solved for arbitrary time-dependent electric and magnetic fields by a new general method. Instead of the usual ansatz: particle velocity = cyclotron velocity + drift velocity the method given makes the ansatz: particle velocity = tensor = cyclotron velocity. The unknown tensor obeys a simple differential equation of the first order which can be generally solved at once. This method is a modification of the variation of constants method for inhomogeneous differential equations. The electromagnetic fields considered must be spatially homogeneous; for (weakly) inhomogeneous fields an iteration procedure of Pytte (1962) may be applied. Some examples are discussed shortly. The Langevin equation treated is completely equivalent to the equation of motion in a magnetohydrodynamic one-fluid theory.     

麦克斯韦方程组的建立及其作用

麦克斯韦提出了描述经典电磁场运动及其与带电粒子相互作用规律的完备方程组,将电学、磁学和光学统一为电磁场动力学理论。这一理论具有洛仑兹协变性和U(1)局域规范不变性,成为构造粒子物理标准模型的经典模板,在物理理论和实验发展中起着不可估量的巨大作用。     

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.     

Nonrelativistic anyons in external electromagnetic field

The first-order, infinite-component field equations we proposed before for nonrelativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.     

The classical equations of motion for a spinning point particle with charge and magnetic moment

The classical, special relativistic equations of motion are derived for a spinning point particle interacting with the electromagnetic field through its charge and magnetic moment. Radiation reaction is included. The energy tensors for the particle and for the field are developed as well-defined distributions; consequently no infinities appear. The magnitude of spin and the rest mass are conserved.     

The motion of a charged particle in magnetostatic and electromagnetic fields

The exact solutions are given of the relativistic equations of motion for both the momentum and displacement of a charged particle which is injected into an arbitrary number of intense electromagnetic waves of any polarization and frequency, including zero, all of which propagate parallel to a uniform magnetostatic field with the speed of light. The solutions are implicit in time.     

On electromagnetic waves by an accelerated charged particle in medium

We have investigated the effects of acceleration of a charged particle on its Cerenkov emission and ionization-losses. We have considered the accelerated motion of a charged particle in an infinite medium with the acceleration parallel to the direction of its motion. We have used the method of Fourier transforms to solve the Maxwell's equations with appropriate current and charge-densities to find electromagnetic fields and hence the force experienced by the incident charge due to its interaction with the medium (dielectric or plasma). The results obtained are general and applicable to any acceleration. In the approximations of ‘small acceleration’ and ‘small interaction time’, we have solved the wave equations and determined electromagnetic potentials. It is found that the acceleration of the charged particle strongly changes both its ionization-loss and Cerenkov emission.     

Covariant description of the spin states of a fermi particle moving in external fields

Covariant operators for the spin of a Fermi particle are considered. The choice of spin integrals of motion is determined for motion in steady isotropie electromagnetic fields. The spin integrals in the presence of an anomalous magnetic moment are examined.