Notes on Fock space

TL;DR

This paper provides a comprehensive overview of Fock space, its related algebras, and their interrelations, including the boson-fermion correspondence and a deformation linked to quantum affine algebras.

Contribution

It offers a self-contained explanation of Fock space and explores the connections between various algebraic structures acting on it, including a novel discussion on deformations.

Findings

Clarifies the structure of Fock space and associated algebras

Details the boson-fermion correspondence

Introduces a deformation related to quantum affine algebras

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).