On the Mickelsson-Faddeev extension and unitary representations

DOI10.1007/BF01218587zbMath0688.22003MaRDI QIDQ1263685

Doug Pickrell

Publication date: 1989

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

zbMATH Keywords

unitary representationcentral chargeKac-Moody groupgauge potentialHamiltonian gauge groupKac-Moody extensionMickelsson-Faddeev extensionnoncentral abelian extension

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Applications of Lie groups to the sciences; explicit representations (22E70) Axiomatic quantum field theory; operator algebras (81T05) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

Related Items (12)

Fermion current algebras and Schwinger terms in \((3+1)\)-dimensions ⋮ Vacuum expectation values of products of chiral currents in \(3+1\) dimensions ⋮ Hilbert space cocycles as representations of \((3+1)\)-D current algebras ⋮ Group actions on C\(^*\)-algebra, 3-cocycles and quantum field theory ⋮ Schwinger terms and cohomology of pseudodifferential operators ⋮ Realizing 3-cocycles as obstructions ⋮ On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations ⋮ Geometry of infinite dimensional Grassmannians and the Mickelsson-Rajeev cocycle ⋮ Projective unitary representations of infinite-dimensional Lie groups ⋮ Fractional loop group and twisted \(K\)-theory ⋮ Universal Schwinger cocycles of current algebras in \((D+1)\)-dimensions: Geometry and physics ⋮ Deformation of current algebras in \(3+1\) dimensions

Cites Work

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• Current algebra representation for the \(3+1\) dimensional Dirac-Yang-Mills theory
• Current algebras in \(d+1\)-dimensions and determinant bundles over infinite-dimensional Grassmannians
• Separable representations for automorphism groups of infinite symmetric spaces
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space

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