Communications in Mathematical Physics

, Volume 330, Issue 3, pp 1293–1326 | Cite as

n-Particle Quantum Statistics on Graphs

  • J. M. Harrison
  • J. P. Keating
  • J. M. Robbins
  • A. SawickiEmail author
Open Access


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.


Homology Group Gauge Potential Star Graph Central Vertex Independent Cycle 
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Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • J. M. Harrison
    • 1
  • J. P. Keating
    • 2
  • J. M. Robbins
    • 2
  • A. Sawicki
    • 2
    • 3
    Email author
  1. 1.Department of MathematicsBaylor UniversityWacoUSA
  2. 2.School of MathematicsUniversity of BristolBristolUK
  3. 3.Center for Theoretical PhysicsPolish Academy of SciencesWarsawPoland

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