Kinematical Theory of Spinning Particles

Rivas, Martı́n

doi:10.1007/0-306-47133-7

Cited by 44 publications

(70 citation statements)

References 32 publications

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“…They have been revisited from time to time by many investigators [11][12][13], including others to be cited below. They are of interest mainly for the insight they bring to the interpretation of quantum mechanics.…”

Section: Classical Particles With Spinmentioning

confidence: 99%

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Zitterbewegung in Quantum Mechanics

Hestenes

2009

Found Phys

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The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.

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Section: Classical Particles With Spinmentioning

confidence: 99%

“…with its "scalar components" F μν given by F μν = γ μ · F · γ ν = γ ν · (γ μ · F ) = (γ ν ∧ γ μ ) · F. (13) Note that the two inner products in the middle term can be performed in either order, so a parenthesis is not needed; also, we use the usual convention for raising and lowering indices.…”

Section: Spacetime Algebramentioning

confidence: 99%

Zitterbewegung in Quantum Mechanics

Hestenes

2009

Found Phys

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“…In this section the electromagnetic field of a luminallycirculating point charge is evaluated explicitly, so that in the next section the magnetic force on the luminallycirculating test charge can be evaluated. Sections III A and III B here reproduce Rivas's work in [7] with notation tailored to support the derivation of the magnetic force of one luminally-circulating charge upon another of Section IV.…”

Section: Retarded Electromagnetic Field Of a Relativistically CImentioning

confidence: 99%

Does Bohm’s Quantum Force Have a Classical Origin?

Lush

2016

Found Phys

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In the de Broglie -Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the Zitterbewegung interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.

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“…But actually this result is puzzling. Whatever the history of the particle, z µ (s), obeying the asymptotic condition (128), the totality of alternating local emissions and absorptions, controlled by the Schott term, is zero, so that the global energy-momentum balance (129) holds true. It is as if the particle takes care on that this totality does not become nonvanishing in the end.…”

Section: Paradoxes and Misconceptionsmentioning

confidence: 99%

Self-interaction in classical gauge theories and gravitation

Kosyakov

2019

Physics Reports

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To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom appearing in the action. We outline the occurrence of topological phases in pure field systems. We show that the rearranged Maxwell-Lorentz electrodynamics is a mathematically consistent and physically satisfactory theory which describes new entities, dressed charged particles and radiation. We extend this analysis to cover different modifications of the Maxwell-Lorentz electrodynamics and the SU(N ) Yang-Mills-Wong theory. We take a brief look at a subtle mechanism of self-interaction in classical strings. Turning to general relativity, we note that the total energy and momentum of a system with nontrivial topological content, such as a black hole, are ambiguous, coordinatizationdependent quantities, which resembles the situation with paradoxical decompositions in the Banach-Tarski theorem.

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Kinematical Theory of Spinning Particles

Cited by 44 publications

References 32 publications

Zitterbewegung in Quantum Mechanics

Zitterbewegung in Quantum Mechanics

Does Bohm’s Quantum Force Have a Classical Origin?

Self-interaction in classical gauge theories and gravitation

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