Fractals, metamorphoses and symmetries in quantum field theory

Quantum Group Symmetries in Conformal Field Theory

Quantum groups play the role of hidden symmetries of some two-dimensional field theories. We discuss how they appear in this role in the Wess-Zumino-Witten model of conformal field theory.

Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

We study space-time symmetries in scalar quantum field theory on an arbitrary static space-time. We first consider Euclidean quantum field theory, and show that the isometry group is generated by one-parameter subgroups which have either selfadjoint or unitary quantizations. We then show that the self-adjoint semigroups thus constructed can be analytically continued to one-parameter unitary gro...

Quantum Symmetries and K-Theory

Modified from Vienna Lectures August 2014 for PiTP, July 2015. VERY ROUGH VERSION: UNDER CONSTRUCTION. Version: July 23, 2015

Symmetries in Conformal Field Theory

Let’s begin by recalling a fact about 2d conformal field theories from Phil’s talk last week. Firstly, we can define a complex semigroup A whose objects are conformal equivalence classes of Riemann surfaces which are diffeomorphic to annuli, equipped with parameterisations of their boundary components, one incoming and one outgoing. The semigroup operation is given by gluing an outgoing to an i...

R – Conformal Symmetries in 2 D Nonlocal Quantum Field Theory , Categorical Representation Theory , and Virasoro Algebra