Cyclic Statistics In Three Dimensions
arXiv:hep-th/0308011 · doi:10.1063/1.1738189
Abstract
While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of ref. [1,2,3]. In this work we demonstrate the existence of ``cyclic'', or , {\it non-permutation group} statistics for a system of n > 2 identical, unknotted rings embedded in . We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.
13 pages, 1 figure, LaTex, minor page reformatting