dorsal/arxiv
View SchemaA semiclassical approach to the Dirac equation
| Authors | Jens Bolte, Stefan Keppeler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811025 |
| URL | https://arxiv.org/abs/quant-ph/9811025 |
| DOI | 10.1006/aphy.1999.5912 |
| Journal | Annals Phys. 274 (1999) 125-162 |
Abstract
We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits.
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"abstract": "We derive a semiclassical time evolution kernel and a trace formula for the\nDirac equation. The classical trajectories that enter the expressions are\ndetermined by the dynamics of relativistic point particles. We carefully\ninvestigate the transport of the spin degrees of freedom along the trajectories\nwhich can be understood geometrically as parallel transport in a vector bundle\nwith SU(2) holonomy. Furthermore, we give an interpretation in terms of a\nclassical spin vector that is transported along the trajectories and whose\ndynamics, dictated by the equation of Thomas precession, gives rise to\ndynamical and geometric phases every orbit is weighted by. We also present an\nanalogous approach to the Pauli equation which we analyse in two different\nlimits.",
"arxiv_id": "quant-ph/9811025",
"authors": [
"Jens Bolte",
"Stefan Keppeler"
],
"categories": [
"quant-ph",
"chao-dyn",
"math-ph",
"math.MP",
"nlin.CD"
],
"doi": "10.1006/aphy.1999.5912",
"journal_ref": "Annals Phys. 274 (1999) 125-162",
"title": "A semiclassical approach to the Dirac equation",
"url": "https://arxiv.org/abs/quant-ph/9811025"
},
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