A note on the Boson-Fermion correspondence and infinite dimensional groups

DOI10.1007/BF01209324zbMath0577.46067MaRDI QIDQ1066062

C. A. Hurst, Alan L. Carey

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

vertex operatorsprojective representation of loop groups

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Applications of Lie groups to the sciences; explicit representations (22E70) Constructive quantum field theory (81T08) Applications of selfadjoint operator algebras to physics (46L60) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Miscellaneous applications of functional analysis (46N99)

Related Items (14)

Temperature states on loop groups, theta functions and the Luttinger model ⋮ On fermionic gauge groups, current algebras and Kac-Moody algebras ⋮ Construction by bosonization of a fermion-phonon model ⋮ Examples of odd index theorems ⋮ Implementability of gauge transformations and quantization of fermions in external fields ⋮ Two types of universal characters and the integrable hierarchies ⋮ Exact solution of a 2D interacting fermion model ⋮ Temperature states on loop groups, boson-fermion correspondence, and a determinant identity ⋮ Steady states and universal conductance in a quenched Luttinger model ⋮ Hilbert \(C^*\)-systems for actions of the circle group ⋮ Unnamed Item ⋮ Infinite dimensional groups and quantum field theory ⋮ Algebras almost commuting with Clifford algebras in a \(II_{\infty}\) factor ⋮ Local anyonic quantum fields on the circle leading to cone-local anyons in two dimensions

Cites Work

• Absence of vacuum polarisation in Fock space
• Representation of nilpotent locally compact groups
• Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
• Basic representations of affine Lie algebras and dual resonance models
• Unitary representations of some infinite dimensional groups
• Automorphisms of the canonical anticommutation relations and index theory
• Quasi-free 'second quantization'
• Multiplier representations of Abelian groups
• Multipliers on Abelian groups
• Fermions and associated bosons of one-dimensional model
• Unnamed Item
• Unnamed Item

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