dorsal/arxiv
View SchemaLocalizing the Relativistic Electron
| Authors | A. J. Bracken, G. F. Melloy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903087 |
| URL | https://arxiv.org/abs/quant-ph/9903087 |
| DOI | 10.1088/0305-4470/32/34/302 |
| Journal | J.Phys.A32:6127-6139,1999 |
Abstract
A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator. It is shown that, although this operator does not represent an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the associated 4-vector density is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive-energy states. A suitable spin operator can be diagonalized at the same time.
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"abstract": "A causally well-behaved solution of the localization problem for the free\nelectron is given, with natural space-time transformation properties, in terms\nof Dirac\u0027s position operator. It is shown that, although this operator does not\nrepresent an observable in the usual sense, and has no positive-energy\n(generalized) eigenstates, the associated 4-vector density is observable, and\ncan be localized arbitrarily precisely about any point in space, at any instant\nof time, using only positive-energy states. A suitable spin operator can be\ndiagonalized at the same time.",
"arxiv_id": "quant-ph/9903087",
"authors": [
"A. J. Bracken",
"G. F. Melloy"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/32/34/302",
"journal_ref": "J.Phys.A32:6127-6139,1999",
"title": "Localizing the Relativistic Electron",
"url": "https://arxiv.org/abs/quant-ph/9903087"
},
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