Noncompact SL(2,ℝ) spin chain View Full Text


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Article Info

DATE

2004-06-18

AUTHORS

Marc Kirch, Alexander N. Manashov

ABSTRACT

We consider the integrable spin chain model — the noncompact SL(2,) spin magnet. The spin operators are realized as the generators of the unitary principal series representation of the SL(2,) group. In an explicit form, we construct -matrix, the Baxter -operator and the transition kernel to the representation of the Separated Variables (SoV). The expressions for the energy and quasimomentum of the eigenstates in terms of the Baxter -operator are derived. The analytic properties of the eigenvalues of the Baxter operator as a function of the spectral parameter are established. Applying the diagrammatic approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the -operator. We show that the transition kernel to the SoV representation is factorized into a product of certain operators each depending on a single separated variable. More... »

PAGES

035

References to SciGraph publications

  • 1981-06. 1/n Expansion: Calculation of the exponents η andν in the order 1/n2 for arbitrary number of dimensions in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2003-10-23. Baxter ℚ-operator and separation of variables for the open SL(2,ℝ) spin chain in JOURNAL OF HIGH ENERGY PHYSICS
  • 1979-08. Quantum inverse problem method. I in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2000-03. Eigenfunctions of GL(N, ℝ) Toda chain: Mellin-Barnes representation in JETP LETTERS
  • 2000-08. On Baxter's Q-Operator for the XXX Spin Chain in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1999-10. Integral Representation for the Eigenfunctions of a Quantum Periodic Toda Chain in LETTERS IN MATHEMATICAL PHYSICS
  • 2003-07-21. Separation of variables for the quantum SL(2,ℝ) spin chain in JOURNAL OF HIGH ENERGY PHYSICS
  • Journal

    TITLE

    Journal of High Energy Physics

    ISSUE

    06

    VOLUME

    2004

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1088/1126-6708/2004/06/035

    DOI

    http://dx.doi.org/10.1088/1126-6708/2004/06/035

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1010404685


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