Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

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     

Invariance identities associated with finite gauge transformations and the uniqueness of the equations of motion of a particle in a classical gauge field

A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations.     

Comparison of algorithms for the symbolic computation of the NP spin coefficients and curvature components

Algorithms for the symbolic computation of the NP spin coefficients and curvature components for a given null coframe based on the structural equations of Cartan and the complex vectorial formalism of Debever are described. The efficiency of the algorithms is compared theoretically and also empirically in a number of test cases using implementations in the computer algebra system Maple. The test results confirm the theoretical superiority of the algorithm based on Debever's formalism over the one based directly on Cartan's first structural equations for the computation of the spin coefficients both with respect to execution time and storage requirements. The algorithm for the computation of the curvature components based on Debever's formalism is generally superior to the one based on Cartan's second structural equations but the advantage is not as marked as for the spin coefficients.     

Particle Spin Described by Quantum Hamilton Equations

The anomalous Zeeman effect made it clear that charged particles like the electron possess a magnetic dipole moment. Classically, this could be understood if the charged particle possesses an eigenrotation, that is, spin. Within Nelson's stochastic mechanics, it was shown that the model of a rotating charged ball is able to reproduce the well-known spin expectation values. This classically motivated model of intrinsic rotation described in terms of a stochastic process is revisited here within the formalism of stochastic optimal control theory. Quantum Hamilton equations (QHE) for spinning particles are derived, which reduce to their classical counterpart in the zero quantum noise limit. These equations enable the calculation of the common spin expectation values without the use of the wave function. They also offer information on the orientation dynamics of the magnetic moment of charged particles beyond the behavior of the spin averages.     

Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

A stochastic model for the dynamics of a classical spin

A stochastic model for the dynamics of a macroscopic or classical spin based on a classical generalized Lagrangian formalism is proposed. The model can be used to describe the evolution of the magnetic moment of superparamagnetic particles. In this sense, it is a generalization of the model proposed by Brown, allowing for fluctuations on the magnitudes of the magnetic moments of the particles. The corresponding covariant Fokker-Planck equation is also obtained.     

Paths of spinning particles in general relativity as geodesics of an Einstein connection

This paper deals with the Papapetrou-Pirani equations of motion for a spinning test particle in general relativity. The motion of the center of mass can be represented by the geodesic equation of an affine connection that is the sum of the Christoffel connection and a tensor that depends on the Riemann-Christoffel curvature tensor, the mass of the particle, its 4-velocity, and its spin tensor. The connection is not unique, and here it is chosen to satisfy one of the basic geometrical principles of Einstein's unified field theory: The symmetric part of the fundamental tensor of the geometry is specified to be the metric tensor of general relativity. The special case of conformally flat space-times is discussed.     

Study of coupling effect on the performance of a spin-current diode: Nonequilibrium Green’s function based model

In this paper, spin-dependent transport through a spin diode composed of a quantum dot coupled to a normal metal and a ferromagnetic lead is studied. The current polarization and the spin accumulation are analyzed using the equations of motion method within the nonequilibrium Green’s function formalism. We present a suitable method for computing Green’s function without carrying out any self-consistent calculation. The influence of coupling strength and magnetic field on the spin current is studied and observed that this device cannot work as a spin diode under certain conditions.     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

The Bargmann-Wigner method in Galilean relativity

The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling.More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.Research supported in part by the U.S. Atomic Energy Commission.     

Clifford's Algebra and a Solution of the Bargmann–Michel–Telegdi Equation

Clifford's algebra of the Minkowski space is constructed in the present paper. A method of solving the equations of motion within the formalism of this algebra is described. A solution of the equation of spin motion (the Bargmann–Michel–Telegdi equation) for the case of motion of a magnetic top in a constant uniform electromagnetic field is derived with the help of the algorithm constructed.     

Moment Method for Spin Analysis of the Pseudoscalar Pair Produced in the Radiative J/ψ Decay

The formalism and technique of the moment method for spin analysis of the boson X in J/ψ→γX,X→P₁P₂ are presented.The analysis technique is cited to study the spin of θ(1720) with Monte Carlo data samples.One finds that the spin of the boson X can be effectively determined by the moment method.As an example,the technique is used to measure the spin of the resonances in the low mass region of J/ψ→γK⁺K^－ channel at BES.It is found that the spin analysis strategy of the moment method is successful.     

Localized magnetic excitations of coupled impurities in a transverse Ising ferromagnet

A Green's function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green's functions are determined in the framework of the Ising model in a transverse field and results are given for the effect of the exchange coupling, position and orientation of the impurities on the spectra of localized spin wave modes.     

On quadrupole and octupole gravitational radiation in the ANK formalism

Following the approach of Adamo–Newman–Kozameh (ANK) we derive the equations of motion for the center of mass and intrinsic angular moment for isolated sources of gravitational waves in axially symmetric spacetimes. The original ANK formulation is generalized so that the angular momentum coincides with the Komar integral for a rotational Killing symmetry. This is done using the Winicour–Tamburino Linkages which yields the mass dipole-angular momentum tensor for the isolated sources. The ANK formalism then provides a complex worldline in a fiducial flat space to define the notions of center of mass and spin. The equations of motion are derived and then used to analyse a very simple astrophysical process where only quadrupole and octupole contributions are included. The results are then compared with those coming from the post newtonian approximation.     

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)     

Current-induced spin polarization and the spin Hall effect: A quasiclassical approach

The quasiclassical Green function formalism is used to describe charge and spin dynamics in the presence of spin-orbit coupling. We review the results obtained for the spin Hall effect on restricted geometries. The role of boundaries is discussed in the framework of spin diffusion equations.     

The application of spin coefficient techniques in the vacuum quadratic Poincaré gauge field theory

The vacuum field equations of the quadratic Poincaré gauge field theory are expressed in the spin coefficient formalism of Newman and Penrose. These are differential identities involving curvature and torsion and, for an NP-type approach, must be combined with the NP-identities in aU ₄ given by Jogia and Griffiths (1980). The use of the formalism is demonstrated in the derivation of some new exact solutions.