New Kinematics (Statistics and Symmetry) in Low-Dimensional QFT with Applications to Conformal QFT2

Abstract

The concepts of field commutation relation, particle statistics and the origin of internal symmetries always have been considered as fundamental in quantum field theory. In the standard Lagrangian approach one usually starts with fields having Fermi- or Bose-statistics which carry an internal compact Lie-group symmetry (i.e. a subgroup of SU n for large enough n). These fields are then “coupled” in order to implement the idea of local interactions in accordance with the Einstein causality of observables. For the most interesting cases of strictly renormalizable interactions (pocessing dimensionless coupling constants) as e.g. “local gauge theories”, there is essentially no non-perturbative analytic result.KeywordsLight ConeBraid GroupTracial StateSuperselection SectorExchange AlgebraThese 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.