Structure of Superselection Sectors in Low-Dimensional Quantum Field Theory

Abstract

The basic principles of relativistic quantum field theory, i.e. locality as an incorporation of Einstein causality and the spectrum condition as a formulation of stability, which are extremely restrictive in 4 dimensional space time admit a richer structure in low dimensions (2 and 3). So particle statistics is in general described by a representation of the braid group instead of the usual Bose and Fermi statistics, statistical weights in cross sections are given in terms of link invariants, and the notion of a group of internal symmetries is generalized to “quantized symmetries”, as quantum groups or Ocneanu’s quantized groups.KeywordsUnitary RepresentationBraid GroupConformal Field TheoryDouble ConeSuperselection SectorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.