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.
Based on joint work with K. Fredenhagen and K.H. Rehren
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Schroer, B. (1990). New Kinematics (Statistics and Symmetry) in Low-Dimensional QFT with Applications to Conformal QFT2 . In: Chau, LL., Nahm, W. (eds) Differential Geometric Methods in Theoretical Physics. NATO ASI Series, vol 245. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-9148-7_13
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