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Symplectic geometry of the Chern-Simons theory

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Integrable Models and Strings

Part of the book series: Lecture Notes in Physics ((LNP,volume 436))

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Abstract

This article is a review of two original papers [1], [2]. We begin with a description of Kirillov symplectic form and quantum mechanics on a coadjoint orbits of a simple Lie group. This theory may be generalized for the case of a Poisson-Lie group. Both these theories are important for understanding of the Chern-Simons model which may be treated as a 3D gauge theory interacting with coadjoint orbits sitting on Wilson lines. Due to topological nature of the Chern Simons theory one can get rid of the gauge fields in exchange of modification of coadjoint theories. We discover that this modification is exactly the same as we find in the Poisson-Lie case.

On leave of absence from Steklov Mathematical Institute, Fontanka 27, St.Petersburg, Russia

Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821-304

On leave of absence from St.-Petersburg University.

Supported in part by 'a Soros Foundation Grant awarded by the American Physical Society.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Uppsala University, Box 803, S-75108, Uppsala, Sweden

    A. Yu. Alekseev & A. Z. Malkin

Authors
  1. A. Yu. Alekseev
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  2. A. Z. Malkin
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Editor information

Anton Alekseev Antero Hietamäki Katri Huitu Alexei Morozov Antti Niemi

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© 1994 Springer-Verlag

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Alekseev, A.Y., Malkin, A.Z. (1994). Symplectic geometry of the Chern-Simons theory. In: Alekseev, A., Hietamäki, A., Huitu, K., Morozov, A., Niemi, A. (eds) Integrable Models and Strings. Lecture Notes in Physics, vol 436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58453-6_5

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  • DOI: https://doi.org/10.1007/3-540-58453-6_5

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  • Print ISBN: 978-3-540-58453-7

  • Online ISBN: 978-3-540-48810-1

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