期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 330, 期 3, 页码 1293-1326出版社
SPRINGER
DOI: 10.1007/s00220-014-2091-0
关键词
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资金
- University of Bristol
- Polish Ministry of Science and Higher Education [N N202 085840]
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.
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