Non-compact Spin Research Articles

Solution of the Odderon Problem for Arbitrary Conformal Weights

A new method is applied to solve the Baxter equation for three coupled, noncompact spins. Due to the equivalence with the system of three reggeized gluons, the intercept of the odderon trajectory is predicted for the first time, as the analytic function of the two relevant parameters.

Quasiclassical QCD pomeron

The Regge behaviour of the scattering amplitudes in perturbative QCD is governed in the generalized leading logarithmic approximation by the contribution of the color-singlet compound states of reggeized gluons. The interaction between reggeons is described by the effective hamiltonian, which in the multi-color limit turns out to be identical to the hamiltonian of the completely integrable one-dimensional XXX Heisenberg magnet of non-compact spin s = 0. The spectrum of the color-singlet reggeon compound states, perturbative pomerons and odderons, is expressed by means of the Bethe ansatz in terms of the fundamental Q-function, which satisfies the Baxter equation for the XXX Heisenberg magnet. The exact solution of the Baxter equation is known only in the simplest case of the compound state of two reggeons, the BFKL pomeron. For higher reggeon states the method is developed which allows to find its general solution as an asymptotic series in powers of the inverse conformal weight of the reggeon states. The quantization conditions for the conserved charges for interacting reggeons are established and an agreement with the results of numerical solutions is observed. The asymptotic approximation of the energy of the reggeon states is defined based on the properties of the asymptotic series, and the intercept of the three-reggeon states, the perturbative odderon, is estimated.

High energy QCD as a completely integrable model

We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin s = 0 and find the conservation laws of the model. A generalized Bethe ansatz is developed for the diagonalization of the hamiltonian and for the calculation of hadron-hadron scattering amplitude.

A noncompact spin model in (2+1) dimensions

A modified version of the Ishimori model endowed with SU(1,1) symmetry is proposed. Some classes of both rational and biperiodic exact singular solutions are obtained. These solutions are characterized by a topological charge.

Remarks on the non-compact spin systems

For an abstract thermodynamically well behaved local specification describing a lattice spin system with non-compact state space, the author gives a short proof of the independence of the limiting thermodynamics on the typical boundary conditions. This general theorem is then applied to superstable and regular spin systems studied by Lebowitz and Presutti (1980) to simplify and clarify their proof. Another application gives the uniqueness theorem for the limiting Gibbs phase for a class (in general non-superstable) of lattice systems with unbounded spins.

Non-compact classical spin models

We analyse classical spin models with fields on the homogeneous spacesO(N,1)/O(N) andO(N, 1)/O(N-1,1) carried by cubic lattices. In particular we study their phase diagrams in the larged or largeN limits. In the case of theO(N, 1)/O(N) model we derive the high temperature expansion. Its coefficients are expressible as expectation values of a nontrivial field model and can therefore only be calculated approximately.

Reflection positivity and models with noncompact spin

Reflection positivity and models with noncompact spin