n-Particle Quantum Statistics on Graphs

Jonathan M Harrison, Jon P Keating, Jonathan M Robbins, Adam Sawicki

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)
346 Downloads (Pure)


Abstract: 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.
Original languageEnglish
Pages (from-to)1293–1326
Number of pages34
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 6 Jun 2014


  • quantum graphs
  • quantum statistics
  • topology of configurations spaces

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