Super boson-fermion correspondence
type: Item
instance of: scholarly article
title: Super boson-fermion correspondence
zbMATH Open document ID: 0625.58041
author: Victor G. Kac
author: Johan W. van de Leur
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74784
review text: We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential noncommutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra \~g\(\ell _{1| 1}\). The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions of all degenerate highest weight representations of \~g\(\ell _{1| 1}\) and of some interesting representations of \(g\ell _{\infty | \infty}({\mathbb{C}})\), and also derive some new combinatorial identities. We hope that this construction will provide a representation theoretical framework for hierarchies of super soliton equations.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 4015778
zbMATH Keywords: super boson-fermion correspondence
zbMATH Keywords: quantum field theory
zbMATH Keywords: bosonic fields
zbMATH Keywords: superbosonic fields
zbMATH Keywords: affine superalgebra
zbMATH Keywords: super fermionization procedure
zbMATH Keywords: super vertex operators
zbMATH Keywords: highest weight representations
zbMATH Keywords: combinatorial identities
MaRDI profile type: Publication
OpenAlex ID: W2322696657
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DOI: 10.5802/AIF.1113
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 4015778