We present a nonperturbative formulation of the anti-Hermitian cubic Reggeon field theory (RFT) in terms of a single field $\chi$. We analyze the structure of RFT as ${\alpha }_0$ is increased above 1 and clarify the relation between the perturbative vacuum and the classical stationary points. A canonical transformation is performed so that the new Hamiltonian depends on the sign of ${\Delta }_0\equiv 1-{\alpha }_0$ only through a potential of the Landau-Ginzburg type. Our one-component theory is normal-ordered with respect to the original Pomeron field without tadpoles, and it allows a path-integral formalism with undistorted contours. For $\frac{\left|{\Delta }_0\right|}{g_0}$ large and ${\Delta }_0<0$, we formulate two different and yet equivalent analog models. We unambiguously derive an analog model in terms of a single classical spin at each rapidity-impact-parameter site. Through the use of an asymmetrical transfer matrix, we obtain a kinklike ground-state configuration for the $D = 0$ model. Alternatively, by going on a lattice for the impact-parameter space only, we arrive at a quantum lattice-spin model. We explicitly demonstrate that the quantum spin model at $D = 0$ is equivalent to the classical lattice spin model.

• Received 4 March 1977

DOI:https://doi.org/10.1103/PhysRevD.16.1186