Introductory lectures on topological quantum field theory

Abstract

Topological quantum field theory (TQFT) is a vast and rich subject that relates in a profound manner physical observables to topological invariants. These lecture notes provide an elementary introduction to the subject. We will introduce Atiyah's axiomatic definition of topological quantum field theories and explain how it provides a particularly intuitive, pictorial representation of the algebraic structure of two-dimensional TQFTs. We also consider Witten's topological twist as a means to obtain so-called cohomological TQFTs. These notes are based on lectures given at the XV Modave Summer School in Mathematical Physics.