Baxter ℚ-operator and separation of variables for the open SL(2,ℝ) spin chain View Full Text


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Article Info

DATE

2003-10-23

AUTHORS

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

ABSTRACT

We construct the Baxter -operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,) spin chain. Applying the diagrammatical 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 the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,) and SL(2,) spin chains. More... »

PAGES

053

References to SciGraph publications

  • 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
  • 1984-10. Factorizing particles on a half-line and root systems in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1985. The quantum Toda chain in NON-LINEAR EQUATIONS IN CLASSICAL AND QUANTUM FIELD THEORY
  • 2002-08. Conserved currents of the three-reggeon interaction in PHYSICS OF ATOMIC NUCLEI
  • 1999-10. Integral Representation for the Eigenfunctions of a Quantum Periodic Toda Chain in LETTERS IN MATHEMATICAL PHYSICS
  • 1985. Special orthogonal polynomial systems mapped onto each other by the Fourier-Jacobi transform in POLYNÔMES ORTHOGONAUX ET APPLICATIONS
  • 2003-07-21. Separation of variables for the quantum SL(2,ℝ) spin chain in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1088/1126-6708/2003/10/053

    DOI

    http://dx.doi.org/10.1088/1126-6708/2003/10/053

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    https://app.dimensions.ai/details/publication/pub.1018228648


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