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The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory

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Abstract:

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,ℝ/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand–Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local Bäcklund transformation. These calculations prepare the theory for an exact canonical quantization.

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Authors and Affiliations

  1. Institut für Physik, Johannes-Gutenberg-Universität Mainz, Staudingerweg 7, D-55099 Mainz, Germany. E-mail: umueller@thep.physik.uni-mainz.de, , , , , , DE

    Uwe Müller

  2. Deutsches Elektronen-Synchrotron DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen, Germany.¶E-mail: weigt@ifh.de, , , , , , DE

    Gerhard Weigt

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  1. Uwe Müller
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  2. Gerhard Weigt
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Received: 9 June 1998 / Accepted: 7 March 1999

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Müller, U., Weigt, G. The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory. Comm Math Phys 205, 421–436 (1999). https://doi.org/10.1007/s002200050684

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  • DOI: https://doi.org/10.1007/s002200050684

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