Superselection structure and statistics in three-dimensional local quantum theory

This paper analyzes the structure of superselection sectors and the statistics of charged fields in general local quantum theories on three-dimensional Minkowski space. The authors find that physical, charged fields may exhibit braid statistics, including non-abelian braid statistics. The authors argue that models with (non-abelian) braid statistics can be constructed from (non-abelian) three-dimensional gauge- and matter fields with a topological Chern-Simons term in the effective gauge field action. It is conceivable that our analysis explains some qualitative aspects of the fractional quantum Hall effect and of certain high Tc superconducting materials, but that remains speculative