dorsal/arxiv
View SchemaThe dynamical equation of the spinning electron
| Authors | Martin Rivas |
|---|---|
| Categories | |
| ArXiv ID | physics/0112005 |
| URL | https://arxiv.org/abs/physics/0112005 |
| DOI | 10.1088/0305-4470/36/16/318 |
| Journal | J.Phys.A36:4703,2003 |
Abstract
We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.
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"abstract": "We obtain by invariance arguments the relativistic and non-relativistic\ninvariant dynamical equations of a classical model of a spinning electron. We\napply the formalism to a particular classical model which satisfies Dirac\u0027s\nequation when quantised. It is shown that the dynamics can be described in\nterms of the evolution of the point charge which satisfies a fourth order\ndifferential equation or, alternatively, as a system of second order\ndifferential equations by describing the evolution of both the center of mass\nand center of charge of the particle. As an application of the found dynamical\nequations, the Coulomb interaction between two spinning electrons is\nconsidered. We find from the classical viewpoint that these spinning electrons\ncan form bound states under suitable initial conditions. Since the classical\nCoulomb interaction of two spinless point electrons does not allow for the\nexistence of bound states, it is the spin structure that gives rise to new\nphysical phenomena not described in the spinless case. Perhaps the paper may be\ninteresting from the mathematical point of view but not from the point of view\nof physics.",
"arxiv_id": "physics/0112005",
"authors": [
"Martin Rivas"
],
"categories": [
"physics.class-ph",
"hep-th",
"physics.gen-ph"
],
"doi": "10.1088/0305-4470/36/16/318",
"journal_ref": "J.Phys.A36:4703,2003",
"title": "The dynamical equation of the spinning electron",
"url": "https://arxiv.org/abs/physics/0112005"
},
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