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Loop Groups and Quantum Fields

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Geometric Analysis and Applications to Quantum Field Theory

Part of the book series: Progress in Mathematics ((PM,volume 205))

Abstract

This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using vertex operators. These examples include the construction and solution of the Luttinger model and other 1+1 dimensional interacting quantum field theories, the construction of anyon field operators on the circle, the 2nd quantization’ of the Calogero—Sutherland model using anyons and the geometric construction of quantum fields on Riemann surfaces. We describe some new results on the elliptic CalogeroSutherland model.

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Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, Adelaide, SA, 5005, Australia

    Alan L. Carey

  2. Mathematical Physics, Physics Department KTH, SCFAB, SE-10691, Stockholm, Sweden

    Edwin Langmann

Authors
  1. Alan L. Carey
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  2. Edwin Langmann
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Editors and Affiliations

  1. Department of Physics and Mathematical Physics, Adelaide, SA, 5005, Australia

    Peter Bouwknegt

  2. Department of Pure Mathematics, University of Adelaide, Adelaide, SA, 5005, Australia

    Peter Bouwknegt  & Siye Wu  & 

  3. Department of Mathematics, University of Colorado, Boulder, CO, 80309-0395, USA

    Siye Wu

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Carey, A.L., Langmann, E. (2002). Loop Groups and Quantum Fields. In: Bouwknegt, P., Wu, S. (eds) Geometric Analysis and Applications to Quantum Field Theory. Progress in Mathematics, vol 205. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0067-3_3

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  • DOI: https://doi.org/10.1007/978-1-4612-0067-3_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6597-9

  • Online ISBN: 978-1-4612-0067-3

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