Introduction to superselection sector theory I

In this series of lectures, I will give an introduction to the
operator-algebraic (Doplicher-Haag-Roberts) approach to study the
superselection sectors of a (2D) gapped quantum spin system. The sectors have a
rich mathematical structure of a braided monoidal category. This category
describes all the algebraic properties of the `anyons' or `charges’ such
quantum spin systems can have. The aim of these lectures is to build up this
theory from first principles, using simple examples of topologically ordered
models to illustrate the main ideas. If time permits, I will elaborate on how
this fits into the larger programme of the classification of gapped phases of
matter, and long-range entangled states in particular. No prior knowledge of
operator algebras or tensor categories is assumed.

Rough plan:
- Lecture 1: Motivation and introduction of basic setting
- Lecture 2 and 3: Building the braided (fusion) category of superselection
sectors
- Lecture 4: Classification of phases and long-range entanglement.