Spin & Statistics in Nonrelativistic Quantum Mechanics, I

Details Spin & Statistics in Nonrelativistic Quantum Mechanics, I Spin & Statistics in Nonrelativistic Quantum Mechanics, I

2002-08-26

arxiv.org/abs/quant-ph/0208151v4

Phys.Lett.A322:47-53,2004

Physics

Quantum Physics

15 pages, revised and polished version

Scientific paper

10.1016/j.physleta.2003.12.051

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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