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

Abstract

We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain 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,C) spin magnet. We argue that this kernel is given by the product of the Baxter Q-operators projected onto a special reference state.

26 pages, Latex style, 9 figures. References corrected, minor stylistic changes, version to be published

References in corpus (3)

• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• High Energy QCD: Stringy Picture from Hidden Integrability

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