General equations of motion for test particles in space-time with torsion

The momentum and spin equations of motion for test particles possessing different spins in space-time with torsion are derived from the most general functional form of _M . The same kinds of equations in general relativity and in Kibble's gauge theory of gravitation are special cases of our equations.     

The motion of charged particles in Kaluza-Klein space-time

The equations of motion for charged particles are derived from the geodesic hypothesis in the five-dimensional Kaluza-Klein theory. It is shown that even within this purely classical framework the theory does not describe low mass charged particles, and that in the background of a Kaluza-Klein monopole, the long range scalr field has striking observable consequences for electron motion, even at very large distances.     

Chaotic motion of dust particles in planetary magnetospheres

We numerically investigate the motion of a charged particle in a planetary magnetosphere using several kinds of equatorial plane phase portraits determined by two dynamical parameters: the charge-to-mass ratio and the z-component of the angular momentum. The dependence of chaos on any of the three factors including the two parameters and the energy is mainly discussed. It is found that increasing the energy or the absolute value of the ratio always causes the extent of chaos. However, chaos is weaker for larger angular momentum. Qualitative interpretations to the results obtained are also given.     

A reconstruction in Minkowskian space-time of Einstein's assembly of test particles

We construct the energy-momentum tensor in Minkowskian space-time for Einstein's collisionless system of test particles moving in concentric circles and obtain the four-force necessary to preserve equilibrium. We derive a tensor field, satisfying the linearized Einstein equations, which is consistent with the applied four-force. If the particles are contained within a sphere, then outside the sphere we show that the tensor field is a linearized Schwarzschild fieldwith a cosmological constant (this constant being the potential energy calculated on the surface of the sphere).     

The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.     

Particle motion in Bell-Szekeres space-time

We solve the geodesies equation for a charged particle in Bell-Szekeres spacetime. In the same geometry we give the test particle solution of Dirac's equation.Supported by the Scientific and Technical Research Council of Turkey (T.B.T.A.K).     

Friction coefficients and directed motion of asymmetric test particles

The behavior of a test particle in a rarefied gas of classical particles is investigated. considering different interaction mechanisms (specular and diffuse reflection, respectively). For large mass ratio between test and gas particles, analytical expressions for the linear friction coefficient are derived. Moreover, the existence of directed motion of asymmetric test particles with distinct initial conditions (but in the absence of any gradients) is shown. The analytical results are supported by a numerical simulation technique applicable to systems with any mass ratio, which is described here in detail.     

Supersymmetric Dirac particles in Riemann-Cartan space-time

A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of and thus complete the partial results of previous WKB calculations. We touch also on such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass.     

Chaotic jets with multifractal space-time random walk

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.     

On the motion of test particles in the field of a plane gravitational wave

The motion of test particles in the field of a plane gravitational wave is studied in order to derive some general properties of such motion, especially the possibilities of repeated meetings of two inertially moving particles.The work was done at Moscow State University, Moscow.     

Relativistic particles on quantum space-time

We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators.     

Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

In the “braneworld scenario” ordinary standard model matter and non-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the ‘bulk’ (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Assuming that the lapse function may either be a constant or a function of both time and of the extra coordinates, we have studied the nature of the geodesics of test particles and photons and have analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.     

Momentum,angular momentum,and equations of motion for test bodies in space-time with torsion

The definitions and transformation properties of momentum and angular momentum of test bodies possessing both macroscopic rotation and net spin are discussed. The equations of motion for momentum and angular momentum of test bodies are derived and written in a covariant form when the energy-momentum tensor is symmetric.     

Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

The infeld/schild approach to the geodesic motion of test particles in general relativity

Test particles are defined and a version of the Infeld/Schild theorem on geodesic motion is presented. The hypotheses of the theorem are discussed in the IPN approximation and in the Weyl static axisymmetric metrics. Initial terms in a series solution of the linearized field equations are found explicitly for a test particle on an arbitrary timelike geodesic.     

Reconstructing space-time from world-lines of charged particles

It is possible to reconstruct a given space-time (M, g) furnished with a 2-form Ω (the electromagnetic strength) from the 6-dimensional manifold parametrizing the world-lines in M of the particles with rest-mass m₀ (or 0) and charge ±e₀ (or 0).