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.
Keywords
Cite
@article{arxiv.hep-th/9310057,
title = {Modular Theory and Symmetry in QFT},
author = {B. Schroer},
journal= {arXiv preprint arXiv:hep-th/9310057},
year = {2008}
}
Comments
35 pages, LaTeX