Notes on Fock space

Abstract

These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebra, a Weyl algebra, an infinite rank matrix algebra, and an affine Kac-Moody algebra. We also discuss how the various algebras are related, and in particular describe the celebrated boson-fermion correspondence. We finish by briefly discussing a deformation of Fock space, which is a representation for the quantized universal enveloping algebra of affine sl(n).

v2:Now 17 pages. Minor corrections and some examples added. v1:15 pages. These notes have been on my webpage for several years but they have recently been revised