Modular Theory and Symmetry in QFT
Abstract
The application of the TomitaTakesaki modular theory to the HaagKastler net approach in QFT yields external (spacetime) symmetries as well as internal ones (internal ``gauge paragroups") and their dual counterparts (the ``super selection paragroup"). An attempt is made to develop a (speculative) picture on ``quantum symmetry" which links spacetime symmetries in an inexorable way with internal symmetries. In the course of this attempt, we present several theorems and in particular derive the KacWakimoto formula which links Jones inclusion indices with the asymptotics of expectation values in physical temperature states. This formula is a special case of a new asymptotic Gibbsstate representation of mapping class group matrices (in a HaagKastler net indexed by intervals on the circle!) as well as braid group matrices.
 Publication:

arXiv eprints
 Pub Date:
 October 1993
 arXiv:
 arXiv:hepth/9310057
 Bibcode:
 1993hep.th...10057S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 35 pages, LaTeX