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Quantization of solitons and the restricted sine-Gordon model

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Abstract

We show how to compute form factors, matrix elements of local fields, in the restricted sine-Gordon model, at the reflectionless points, by quantizing solitons. We introduce (quantum) separated variables in which the Hamiltonians are expressed in terms of (quantum) τ-functions. We explicitly describe the soliton wave functions, and we explain how the restriction is related to an unusual hermitian structure. We also present a semi-classical analysis which enlightens the fact that the restricted sine-Gordon model corresponds to an analytical continuation of the sine-Gordon model, intermediate between sine-Gordon and KdV.

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Author notes

  1. F. A. Smirnov

    Present address: Steklov Mathematical Institute, Fontanka 27, 191011, St. Petersburg, Russia

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Tour 16 1er étage, 4 place Jussieu, 75252, Paris cedex 05, France

    O. Babelon (Membre du CNRS) & F. A. Smirnov

  2. Service de Physique Théorique de Saclay, F-91191, Gif-sur-Yvette, France

    D. Bernard

Authors
  1. O. Babelon
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  2. D. Bernard
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  3. F. A. Smirnov
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Additional information

Communicated by G. Felder

Laboratoire associé au CNRS.

Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique.

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Babelon, O., Bernard, D. & Smirnov, F.A. Quantization of solitons and the restricted sine-Gordon model. Commun.Math. Phys. 182, 319–354 (1996). https://doi.org/10.1007/BF02517893

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  • DOI: https://doi.org/10.1007/BF02517893

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