Title:	Cyclic statistics in three dimensions
Authors:	Surya, Sumati
Issue Date:	Jun-2004
Publisher:	The American Institute of Physics
Citation:	Journal of Mathematical Physics, 2004, Vol.45, p2515-2525
Abstract:	The existence of anyons in two-dimensional systems is a well-known example of nonpermutation group statistics. In higher dimensions, however, it is expected that statistics is dictated solely by representations of the permutation group. Using basic elements from representation theory we show that this expectation is false in three-dimensions for a certain nongravitational system. Namely, we demonstrate the existence of "cyclic," or [openface Z]n, nonpermutation group statistics for a system of n>2 identical, unknotted rings embedded in [openface R]3. We make crucial use of a theorem due to Goldsmith in conjunction with the Fuchs–Rabinovitch relations for the automorphisms of the free product group on n elements.
URI:	http://hdl.handle.net/2289/1245
ISSN:	0022-2488
Alternative Location:	http://link.aip.org/link/?jmp/45/2515
Copyright:	(2004)American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Appears in Collections:	Research Papers (TP)

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