On the Possible Trajectories of Particles with Spin. III. Particles in the Stationary Homogeneous Electric Field (original) (raw)

On the Possible Trajectories of Spinning Particles. I. Free Particles

By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as well as by two pseudo vectors one of which is easily associated with external magnetic field, and another still remains undetermined. The equations give a possibility to describe the motion of both massive and massless particles with spin. All solutions of the equations of motion in the absence of external fields were found, and besides, we give more precise definition of a free object. It turns out that the massive particles always possess a longitudinal polarization. There are possible transversal motions of the following types: 1) oscillatory motion with proper frequency, 2) circular motion, and 3) complicated motion along rosette trajectories round the center of inertia with the velocity, varying in the limits v v v  min max. Free massless particles can either fluctuate or move along complicated paths around fixed centers of balance, when the spin of the particles can have any direction. PACS numbers: 14.60Cd, 41.90+e, 45.20.–d, 45.50.–j

Kinematical Theory of Spinning Particles

Time average retarded magnetic field < Br (r) > along the directions θ = 0, π/3, π /4 and π/6 a n d its behavior at r = 0. For θ = π /2 it vanishes everywhere. Time average retarded magnetic field < Bθ(r) > along the directions θ = 0, /3, π π/4 and π/6 a n d its behavior at r = 0. Time average radial component < E r (r) > of the advanced electric field in the directions θ = 0,π /3, π/4 and π/6. Electron charge motion in the C.M. frame. A basis for vectors (a) and bivectors (pseudovectors) (b) of Pauli algebra. Triangular potential barrier. Electron beam into a potential barrier. A classical spinless electron never crosses the dotted line. A spinning particle of the same energy might cross the barrier. Potential Energy of an α-particle in the electric field of a nucleus. Kinetic Energy during the crossing for the values a = b = 1. Kinetic Energy during the crossing for the values a = 1, b = 10. Classical and Quantum Probability of crossing for different potentials. Classical Limit of Quantum Mechanics.

The Spinning Particles – Classical Description

arXiv: Classical Physics, 2019

The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes non-linear. Nevertheless the equations of motion are analyzed in details and solved numerically. In either case the trajectories are ilustrated and their properties are disussed. There is also discussion of possible physical quantities associated with the spinning motions. Among others: the size of particles and their gyromagnetic ratios. Finally, some possible, speculative explanations of the properties of the Universe are proposed: the origin and nature of dark matter and lack of the equilibrium bettween mater and anti-matter.

Dynamics of an active magnetic particle in a rotating magnetic field

Physical Review E, 2006

The motion of an active ͑self-propelling͒ particle with a permanent magnetic moment under the action of a rotating magnetic field is considered. We show that below a critical frequency of the external field the trajectory of a particle is a circle. For frequencies slightly above the critical point the particle moves on an approximately circular trajectory and from time to time jumps to another region of space. Symmetry of the particle trajectory depends on the commensurability of the field period and the period of the orientational motion of the particle. We also show how our results can be used to study the properties of naturally occurring active magnetic particles, so-called magnetotactic bacteria.

Motion of Charged Spinning Particles in a Unified Field

Advances in High Energy Physics, 2021

Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in a gravitational field. The new method used for derivation, the Bazanski method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.

Equations of motion for spinning particles in external electromagnetic and gravitational fields

Physical Review D, 1993

The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin components are automatically satisfied. In general the spin is not Fermi-Walker transported nor does the position follow a geodesic, although the deviations are small for most situations.

On the Kinematics of the Centre of Charge of an Elementary Spinning Particle

AIP Conference Proceedings, 2009

In particle physics, most of the classical models consider that the centre of mass and centre of charge of an elementary particle, are the same point. This presumes some particular relationship between the charge and mass distribution, a feature which cannot be checked experimentally. In this paper we give three different kinds of arguments suggesting that, if assumed different points, the centre of charge of an elementary spinning particle moves in a helical motion at the speed of light, and it thus satisfies, in general, a fourth order differential equation. If assumed a kind of rigid body structure, it is sufficient the description of the centre of charge to describe also the evolution of the centre of mass and the rotation of the body. This assumption of a separation betwen the centre of mass and centre of charge gives a contribution to the spin of the system and also justifies the existence of a magnetic moment produced by the relative motion of the centre of charge. This corresponds to an improved model of a charged elementary particle, than the point particle case. This means that a Lagrangian formalism for describing elementary spinning particles has to depend, at least, up to the acceleration of the position of the charge, to properly obtain fourth order dynamical equations. This result is compared with the description of a classical Dirac particle obtained from a general Lagrangian formalism for describing spinning particles.

Hydrodynamics of Spinning Particles

1998

In this note, we first obtain the decomposition of the non-relativistic field velocity into the classical part (i.e., the velocity w=p/m OF the center-of-mass (CM), and the so-called quantum part (i.e., the velocity V of the motion IN the CM frame (namely, the internal spin-motion or Zitterbewegung), these two parts being orthogonal. Our starting point is the Pauli current. Then, by inserting such a composite expression of the velocity into the kinetic energy term of the non-relativistic newtonian lagrangian, we get the appearance of the so-called "quantum potential" (which makes the difference between classical and quantum behaviour) as a pure consequence of the internal motion. Such a result carries further evidence about the possibility that the quantum behaviour of micro-systems be a direct consequence of the fundamental existence of spin.