Quantum indistinguishability from general representations of SU(2n)

JM Harrison, JM Robbins

Research output: Contribution to journalArticle (Academic Journal)

3 Citations (Scopus)

Abstract

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. London Ser. A 453, 1771-1790 (1997)] is generalized within a group-theoretical framework. The construction of Berry and Robbins is reformulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both Bose and Fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalized) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)xU(n). (C) 2004 American Institute of Physics.
Translated title of the contributionQuantum indistinguishability from general representations of SU(2n)
Original languageEnglish
Pages (from-to)1332 - 1358
Number of pages27
JournalJournal of Mathematical Physics
Volume45 (4)
DOIs
Publication statusPublished - Apr 2004

Bibliographical note

Publisher: American Institute of Physics
Other identifier: IDS Number: 805BW

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