Abstract :
The equivalence is found between high-energy QCD in the generalized leading logarithmic approximation and the one-dimensional Heisenberg magnet. According to Regge theory, the high-energy asymptotics of hadronic scattering amplitudes are related to singularities of partial waves in the complex angular momentum plane. In QCD, the partial waves are determined by nontrivial two-dimensional dynamics of the transverse gluonic degrees of freedom. The “bare” gluons interact with each other to form a collective excitation, the Reggeon. The partial waves of the scattering amplitude satisfy the Bethe-Salpeter equation whose solutions describe the color singlet compound states of Reggeons - Pomeron, Odderon and higher Reggeon states. We show that the QCD Hamiltonian for reggeized gluons coincides in the multi-color limit with the Hamiltonian of XXX Heisenberg magnet for spin s = 0 and spin operators being the generators of the conformal SL(2,C) group. As a result, the Schrödinger equation for the compound states of Reggeons has a sufficient number of conservation laws to be completely integrable. A generalized Bethe ansatz is developed for the diagonalization of the QCD Hamiltonian and for the calculation of hadron-hadron scattering. Using the Bethe Ansatz solution of high-energy QCD we investigate the properties of the Reggeon compound states which govern the Regge behavior of the total hadron-hadron cross sections and the small-x behavior of the structure functions deep inelastic scattering.
