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Problems with Using Separated Variables for Computing Expectation Values for Higher Ranks

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Abstract

We consider the simplest classical integrable model corresponding to a non-hyperelliptic spectral curve. We show that a certain complicated integral occurs when computing the average of observables in this model. This integral does not factorise. Since similar problems should also exist in the quantum case, we think that a serious question arises of how to deal with these integrals.

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Authors and Affiliations

  1. Départment de Physique, École Normale Supérieure, 75005, Paris, France

    David Martin

  2. Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Tour 13, 4er étage, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Fedor Smirnov

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  1. David Martin
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  2. Fedor Smirnov
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Correspondence to Fedor Smirnov.

Additional information

D. Martin: The work was conducted while this author was doing an internship at LPTHE. F. Smirnov: Membre du CNRS.

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Martin, D., Smirnov, F. Problems with Using Separated Variables for Computing Expectation Values for Higher Ranks. Lett Math Phys 106, 469–484 (2016). https://doi.org/10.1007/s11005-016-0823-0

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  • DOI: https://doi.org/10.1007/s11005-016-0823-0

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