  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.
