One-component formulation of Reggeon field theory

Abstract

We present a nonperturbative formulation of the anti-Hermitian cubic Reggeon field theory (RFT) in terms of a single field $\ensuremath{\chi}$. We analyze the structure of RFT as ${\ensuremath{\alpha}}_{0}$ 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 ${\ensuremath{\Delta}}_{0}\ensuremath{\equiv}1\ensuremath{-}{\ensuremath{\alpha}}_{0}$ 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 $\frac{|{\ensuremath{\Delta}}_{0}|}{{g}_{0}}$ large and ${\ensuremath{\Delta}}_{0}<0$, 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.