In the book of Haag [Local Quantum Physics (Springer Verlag, Berlin, 1992)] about local
quantum field theory the main results are obtained by the older methods of C*-and W …

The general theory of superselection sectors is shown to provide almost all the structure
observed in two-dimensional conformal field theories. Its application to two-dimensional …

The theory of superselection sectors is generalized to situations in which normal statistics
has to be replaced by braid group statistics. The essential role of the positive Markov trace of …

We identify the statistical dimension of a superselection sector in a local quantum field
theory with the square root of the index of a localized endomorphism of the quasi-local C …

It is shown that the theory of the quantum Hall effect is closely related to Chern-Simons
gauge theory and to rational conformal field theory. In particular, the equations of classical …

We define and study two-dimensional, chiral conformal field theory by the methods of
algebraic field theory. We start by characterizing the vacuum sectors of such theories and …

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the
circle with central charge c less than 1. The irreducible ones are in bijective correspondence …

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain
energy bounds and a strong form of locality and call them strongly local. We present a …

We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-
system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove …

We prove the equality between the statistics phase and the conformal univalence for a
superselection sector with finite index in Conformal Quantum Field Theory on S 1. A relevant …