Noncompact Heisenberg spin magnets from high-energy QCD - I. Baxter Q-operator and separation of variables

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 wel l-known homogeneous Heisenberg spin magnet to infinite-dimensional represen tations of the SL(2, C) group and can be reformulated within the quantum in verse 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 mod el and show how it can be used to determine the energy spectrum. We apply S klyanin's method of the separated variables to obtain an integral represent ation for the eigenfunctions of the Hamiltonian. We demonstrate that the la nguage of Feynman diagrams supplemented with the method of uniqueness provi de a powerful technique for analyzing the properties of the model. (C) 2001 Elsevier Science B.V. All rights reserved.