Ordered phase in Reggeon field theory

Abstract

We study the ordered phase of Reggeon field theory taking into account both the three- and four-Reggeon couplings. We find that for a range of parameters the ground state of the system is doubly degenerate. For a special value of the bare intercept the non-Hermitian Reggeon field theory Hamiltonian is related by a similarity transformation to a Hermitian one. The Hamiltonian formulation of the theory is therefore on a good footing, and we are able to construct the quantum ground states and study in detail how the ordered phase of Reggeon field theory differs from that of a conventional theory. We discuss a number of possible definitions of the Pomeron Green's functions, and show that for all physically acceptable ones the intercept of the Pomeranchuk singularity is exactly equal to one in the ordered phase. We perform an approximate calculation of the scattering amplitude in one transverse dimension directly in the continuum theory. We find, in agreement with previous spin-model calculations, that the scattering amplitude corresponds to a gray disk with a radius proportional to the log of the energy. Our approximate solution does not satisfy the constraints of t-channel unitarity, and we point out why the usual proof ofmore » unitarity will not go through in the exact theory.« less