dorsal/arxiv
View SchemaSpin & Statistics in Nonrelativistic Quantum Mechanics, I
| Authors | Bernd Kuckert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208151 |
| URL | https://arxiv.org/abs/quant-ph/0208151 |
| DOI | 10.1016/j.physleta.2003.12.051 |
| Journal | Phys.Lett.A322:47-53,2004 |
Abstract
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J the total (i.e., spin plus orbital) angular momentum of a single particle, and denote by j the total angular momentum of the corresponding two-particle system with respect to its center of mass. In three spatial dimensions, write J_z and j_z for the z-components of these vector operators. In two spatial dimensions, the spin statistics connection holds if and only if there exists a unitary operator U such that j=2UJU^*. In three dimensions, the analogous relation cannot hold as it stands, but restricting it to an appropriately chosen subspace of the state space yields a sufficient and necessary condition for the spin-statistics connection.
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"abstract": "A necessary and sufficient condition for Pauli\u0027s spin-statistics relation is\ngiven for nonrelativistic anyons, bosons, and fermions in two and three spatial\ndimensions.\n For any point particle species in two spatial dimensions, denote by J the\ntotal (i.e., spin plus orbital) angular momentum of a single particle, and\ndenote by j the total angular momentum of the corresponding two-particle system\nwith respect to its center of mass. In three spatial dimensions, write J_z and\nj_z for the z-components of these vector operators.\n In two spatial dimensions, the spin statistics connection holds if and only\nif there exists a unitary operator U such that j=2UJU^*. In three dimensions,\nthe analogous relation cannot hold as it stands, but restricting it to an\nappropriately chosen subspace of the state space yields a sufficient and\nnecessary condition for the spin-statistics connection.",
"arxiv_id": "quant-ph/0208151",
"authors": [
"Bernd Kuckert"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1016/j.physleta.2003.12.051",
"journal_ref": "Phys.Lett.A322:47-53,2004",
"title": "Spin \u0026 Statistics in Nonrelativistic Quantum Mechanics, I",
"url": "https://arxiv.org/abs/quant-ph/0208151"
},
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