Spin & Statistics in Nonrelativistic Quantum Mechanics, I
摘要
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.
引用
@article{arxiv.quant-ph/0208151,
title = {Spin & Statistics in Nonrelativistic Quantum Mechanics, I},
author = {Bernd Kuckert},
journal= {arXiv preprint arXiv:quant-ph/0208151},
year = {2008}
}
备注
15 pages, revised and polished version