Yegor Zenkevich : Free field realizations (mini-course), lectures 2

Abstract

Symmetry is key to understanding quantum field theories (QFTs). Usually by a symmetry of a theory one means an algebra acting on its Hilbert space. In this mini-course we will consider the simplest examples of theories in which such algebraic structure arises, namely free QFTs. We will start with free field realizations of classical Lie algebras, generalize them to affine Lie algebras and finally to quantum toroidal algebras. There will be lots of excercises.