We define chiral vertex operators and duality matrices and review the fundamental identities
they satisfy. In order to understand the meaning of these equations, and therefore of …

REMARKS ON THE CANONICAL QUANTIZATION OF THE CHERN-SIMONS-WITTEN
THEORY 1. Introduction Recently, Wltten [1] has shown that Cher Page 1 Nuclear Physics B326 …

We discuss constraints on the operator product coefficients in diagonal and nondiagonal
rational conformal field theories. Nondiagonal modular invariants always arise from …

It is known that the Jones polynomial of knot theory, and its generalizations, are closely
related to the integrable “vertex models” of two-dimensional statistical mechanics, and to …

We use the conformal bootstrap equations to study the non-perturbative gravitational
scattering between infalling and outgoing particles in the vicinity of a black hole horizon in …

The Yang-Baxter algebras (YBA) are introduced in a general framework stressing their
power to exactly solve the lattice models associated to them. The algebraic Bethe Ansatz is …

This book reviews recent results on low-dimensional quantum field theories and their
connection with quantum group theory and the theory of braided, balanced tensor …

We show that the duality properties of Rational Conformal Field Theories follow from the
defining relations and the representation theory of quantum groups. The fusion and braiding …

We present recent results on the statistics in low-dimensional quantum field theory. They are
described by unitary representations of the braid group. We discuss the structure of the" …

We define generalised chiral vertex operators covariant under the Ocneanu “double triangle
algebra” A, a novel quantum symmetry intrinsic to a given rational 2d conformal field theory …