Notes on Fock space

Peter Tingley

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arXiv · 2211.12463

Notes on Fock space

Peter Tingley

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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).

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Peter Tingley. 2023-10-17. Notes on Fock space. https://arxiv.org/abs/2211.12463

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