Modular Theory and Symmetry in QFT
Abstract
The application of the Tomita-Takesaki modular theory to the Haag-Kastler net approach in QFT yields external (space-time) symmetries as well as internal ones (internal ``gauge para-groups") and their dual counterparts (the ``super selection para-group"). An attempt is made to develop a (speculative) picture on ``quantum symmetry" which links space-time symmetries in an inexorable way with internal symmetries. In the course of this attempt, we present several theorems and in particular derive the Kac-Wakimoto 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 Gibbs-state representation of mapping class group matrices (in a Haag-Kastler net indexed by intervals on the circle!) as well as braid group matrices.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 1993
- DOI:
- 10.48550/arXiv.hep-th/9310057
- arXiv:
- arXiv:hep-th/9310057
- Bibcode:
- 1993hep.th...10057S
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 35 pages, LaTeX