Introduction to simple integrable models of quantum field theory

Abstract

We summarize recent developments in the relationship between exactly solvable models of statistical physics and quantum field theory. After a short introduction to critical phenomena, we review the framework for quantum spin models and sketch the solution of simple models. We describe the Luttinger model and its gauged version, the Luttinger-Schwinger model. We use Boson-Fermion correspondence to solve these models and show how one can calculate Green functions. Next, we focus on algebraic aspects of quantum spin models. The structure of quantum integrability leads to the Yang-Baxter equation and eventually gives us a link to the modern developments of quantum geometry.