A note on the Boson-Fermion correspondence and infinite dimensional groups
type: Item
instance of: scholarly article
title: A note on the Boson-Fermion correspondence and infinite dimensional groups
zbMATH Open document ID: 0577.46067
DOI: 10.1007/BF01209324
author: C. A. Hurst
author: A. L. Carey
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: A rigorous construction of certain formulae associated with the names of the physicists Skyrme, Dell-Antonio, Frishman, Zwanziger, Coleman and Mandelstam is given. The construction is motivated in part by the vertex operators used by \textit{G. B. Segal} [Commun. Math. Phys. 80, 301-342 (1981; Zbl 0495.22017)] to construct projective representation of loop groups and is a group theoretical version of the affine Lie algebra approach of \textit{I. B. Frenkel} [J. Funct. Anal. 44, 259-327 (1981; Zbl 0479.17003)] to similar questions. Subsequent work (currently in preprint form) of one of the authors (A.L.C.) with S.N.M. Ruijsenaars generalises these results to construct type III representations of affine Lie algebras.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 3923464
zbMATH Keywords: vertex operators
zbMATH Keywords: projective representation of loop groups
MaRDI profile type: Publication
cites work: Basic representations of affine Lie algebras and dual resonance models
cites work: Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
cites work: Unitary representations of some infinite dimensional groups
cites work: Automorphisms of the canonical anticommutation relations and index theory
cites work: Absence of vacuum polarisation in Fock space
cites work: Q5660202
cites work: Multiplier representations of Abelian groups
cites work: Representation of nilpotent locally compact groups
cites work: Multipliers on Abelian groups
cites work: Quasi-free 'second quantization'
cites work: Fermions and associated bosons of one-dimensional model
cites work: Q4059459
description: scientific article; zbMATH DE number 3923464