Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-07-23
Nucl.Phys. B617 (2001) 375-440
Physics
High Energy Physics
High Energy Physics - Theory
61 pages, 19 figures; version to appear in Nucl.Phys.B
Scientific paper
10.1016/S0550-3213(01)00457-6
We analyze a completely integrable two-dimensional quantum-mechanical model that emerged in the recent studies of the compound gluonic states in multi-color QCD at high energy. The model represents a generalization of the well-known homogenous Heisenberg spin magnet to infinite-dimensional representations of the SL(2,C) group and can be reformulated within the Quantum Inverse Scattering Method. Solving the Yang-Baxter equation, we obtain the R-matrix for the SL(2,C) representations of the principal series and discuss its properties. We explicitly construct the Baxter Q-operator for this model and show how it can be used to determine the energy spectrum. We apply Sklyanin's method of the Separated Variables to obtain an integral representation for the eigenfunctions of the Hamiltonian. We demonstrate that the language of Feynman diagrams supplemented with the method of uniqueness provide a powerful technique for analyzing the properties of the model.
Derkachov Sergey E.
Korchemsky Gregory P.
Manashov Alexander N.
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