dorsal/arxiv
View SchemaZitterbewegung and semiclassical observables for the Dirac equation
| Authors | Jens Bolte, Rainer Glaser |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402154 |
| URL | https://arxiv.org/abs/quant-ph/0402154 |
| DOI | 10.1088/0305-4470/37/24/012 |
| Journal | J. Phys. A: Math. Gen. 37 (2004) 6359-6373 |
Abstract
In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity.
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"abstract": "In a semiclassical context we investigate the Zitterbewegung of relativistic\nparticles with spin 1/2 moving in external fields. It is shown that the\nanalogue of Zitterbewegung for general observables can be removed to arbitrary\norder in \\hbar by projecting to dynamically almost invariant subspaces of the\nquantum mechanical Hilbert space which are associated with particles and\nanti-particles. This not only allows to identify observables with a\nsemiclassical meaning, but also to recover combined classical dynamics for the\ntranslational and spin degrees of freedom. Finally, we discuss properties of\neigenspinors of a Dirac-Hamiltonian when these are projected to the almost\ninvariant subspaces, including the phenomenon of quantum ergodicity.",
"arxiv_id": "quant-ph/0402154",
"authors": [
"Jens Bolte",
"Rainer Glaser"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1088/0305-4470/37/24/012",
"journal_ref": "J. Phys. A: Math. Gen. 37 (2004) 6359-6373",
"title": "Zitterbewegung and semiclassical observables for the Dirac equation",
"url": "https://arxiv.org/abs/quant-ph/0402154"
},
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