Quantum Symmetry in Quantum Theory

Abstract

The authors introduce what they claim to be ``the most generalalgebraic structures which admit a physical interpretation assymmetries''. They call these structures weak quasi Hopfalgebras, which are obtained from the quasi Hopf algebras ofDrinfeld by truncation, an operation motivated by the authors'experience with conformal field theories. After succinctlyreviewing standard symmetries in a setting appropriate for thisgeneralization, the authors explain how weak quasi Hopf algebrascan be interpreted as symmetries and then provide an example bytruncating the quasitriangular Hopf algebraU\sb q({\rm sl}\sb 2). They then discuss the chiral Isingmodel, which motivated the introduction of these new structures,since, as shown by them [Phys. Lett. B 267 (1991), no. 2, 207213; MR \Cite{Mack91:Quasi:207--213}[92g:81087]], this modeladmits the example of weak quasi Hopf algebras previouslyconstructed as a symmetry in precisely the sense they definedearlier in the paper. Finally, they show how algebraic quantumfield theoretical techniques can be used in the Wess ZuminoNovikov Witten models to construct associated Bosefields.\par {For the entire collection see MR 93h:81002.}