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Poisson structure and quantization of Chern-Simons theory

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Quantization of Singular Symplectic Quotients

Part of the book series: Progress in Mathematics ((PM,volume 198))

Abstract

In this note we review some work on the Poisson structure and on the quantization of 2 + 1 dimensional Chern-Simons theory or, in more mathematical terms, of the moduli space of flat connections over a 2-dimensional surface ∑. This moduli space is one of the most important examples of a singular symplectic space. Our description focuses on the combinatorial approach in which the surface ∑ is replaced by a fat graph. Due to the topological nature of the theory, this finite model is exact and allows to recover a number of important results on Chern-Simons theory.

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Author information

Authors and Affiliations

  1. MPI für Gravitationsphysik, Albert-Einstein-Institut, Am Mühenberg 1, D-14476, Golm, Germany

    Volker Schomerus

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  1. Volker Schomerus
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Editor information

Editors and Affiliations

  1. Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    N. P. Landsman

  2. Mathematisch-Naturwissenschaftliche Fakultät II Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Pflaum

  3. Fakultät für Mathematik und Informatik, Universität Mannheim, D7, 27, 68131, Mannheim, Germany

    M. Schlichenmaier

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© 2001 Springer Basel AG

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Schomerus, V. (2001). Poisson structure and quantization of Chern-Simons theory. In: Landsman, N.P., Pflaum, M., Schlichenmaier, M. (eds) Quantization of Singular Symplectic Quotients. Progress in Mathematics, vol 198. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8364-1_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8364-1_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9535-4

  • Online ISBN: 978-3-0348-8364-1

  • eBook Packages: Springer Book Archive

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