Structure of Superselection Sectors in Low-Dimensional Quantum Field Theory
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 Representation Braid Group Conformal Field Theory Double Cone Superselection Sector
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