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Current Algebras as Hilbert Space Operator Cocycles

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Noncompact Lie Groups and Some of Their Applications

Part of the book series: NATO ASI Series ((ASIC,volume 429))

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Abstract

Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, SF-40100, Jyväskylä, Finland

    Jouko Mickelsson

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  1. Jouko Mickelsson
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Editors and Affiliations

  1. Division of Mathematics, University of Texas, San Antonio, Texas, USA

    Elizabeth A. Tanner  & Raj Wilson  & 

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© 1994 Springer Science+Business Media Dordrecht

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Mickelsson, J. (1994). Current Algebras as Hilbert Space Operator Cocycles. In: Tanner, E.A., Wilson, R. (eds) Noncompact Lie Groups and Some of Their Applications. NATO ASI Series, vol 429. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1078-5_25

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  • DOI: https://doi.org/10.1007/978-94-011-1078-5_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4470-7

  • Online ISBN: 978-94-011-1078-5

  • eBook Packages: Springer Book Archive

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