Spin & Statistics in Nonrelativistic Quantum Mechanics, I

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dc.creatorKuckert, Bernd
dc.date2002-08-26
dc.date2003-11-07
dc.date.accessioned2026-07-07T11:32:53Z
dc.date.available2026-07-07T11:32:53Z
dc.descriptionA 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.
dc.description15 pages, revised and polished version
dc.identifierhttps://arxiv.org/abs/quant-ph/0208151
dc.identifierhttp://arxiv.org/abs/quant-ph/0208151
dc.identifierPhys.Lett.A322:47-53,2004
dc.identifierdoi:10.1016/j.physleta.2003.12.051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197752
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleSpin & Statistics in Nonrelativistic Quantum Mechanics, I
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