BRAID GROUP STATISTICS IN TWO-DIMENSIONAL QUANTUM FIELD THEORY

Braid group statistics in two-dimensional quantum field theory

Within the framework of algebraic quantum field theory, we construct explicitly localized morphisms of a Haag-Kastler net in 1 + 1dimensional Minkowski space showing abelian braid group statistics. Moreover, we investigate the scattering theory of the corresponding quantum fields.

Mutual statistics, braid group, and the fractional quantum Hall effect

We show that the notion of mutual statistics arises naturally from the representation theory of the braid group over the multi-sheeted surface. A Hamiltonian which describes particles moving on the double-sheeted surface is proposed as a model for the bilayered fractional quantum Hall effect (FQHE) discovered recently. We explicitly show that the quasi-holes of the bilayered Hall fluid display ...

Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory

Path Integration in Two-dimensional Topological Quantum Field Theory

A positive, di eomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure give the two-dimensional axiomatic topological quantum eld theories,...

Quantum Teichmüller Theory and Representations of the Pure Braid Group

We adapt some of the methods of quantum Teichmüller theory to construct a family of representations of the pure braid group of the sphere. This article presents a variation of the constructions of [2, 3] on the finite-dimensional representation theory of the quantum Teichmüller space. In these two earlier articles, the author and his collaborators considered the quantum Teichmüller space T S of...