Separation of variables for the quantum SL(2,ℝ) spin chain View Full Text


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Article Info

DATE

2003-07-21

AUTHORS

Sergey É. Derkachov, Gregory P. Korchemsky, Alexander N. Manashov

ABSTRACT

We construct a representation of the Separated Variables (SoV) for the quantum SL(2,) Heisenberg closed spin chain following the Sklyanin's approach and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure defining the scalar product in the SoV representation and demonstrate that the language of Feynman diagrams is extremely useful in establishing various properties of the model. The kernel of the unitary transformation to the SoV representation is described by the same ``pyramid diagram'' as appeared before in the SoV representation for the SL(2,) spin magnet. We argue that this kernel is given by the product of the Baxter -operators projected onto a special reference state. More... »

PAGES

047

References to SciGraph publications

  • 2002-05-29. High Energy QCD: Stringy Picture from Hidden Integrability 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
  • 1981-09. Yang-Baxter equation and representation theory: I in LETTERS IN MATHEMATICAL PHYSICS
  • 1999-10. Integral Representation for the Eigenfunctions of a Quantum Periodic Toda Chain in LETTERS IN MATHEMATICAL PHYSICS
  • 1983-11. Local Hamiltonians for integrable quantum models on a lattice in THEORETICAL AND MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1088/1126-6708/2003/07/047

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    http://dx.doi.org/10.1088/1126-6708/2003/07/047

    DIMENSIONS

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