Classical kinks and their quantization in supercritical Reggeon field theory

Abstract

The existence of kink states in supercritical reggeon field theory ( α(0) > α c) is related to the expanding disc behaviour previously found in a lattice approximation. The classical solitary waves of RFT with α(0) − 1 = μ > 0 are classified, for the case of a one-dimensional impact parameter space ( D = 1). We find kink-like solutions corresponding to a range of velocities up to a critical one for which the solution has a phonon-like dispersion law (zero mass). The general methods of kink quantization are adapted to RFT. By then quantizing the theory around the solution with critical velocity we are able to give the low-lying spectrum and to construct the quantum kink states, which in RFT are connected to the vacuum by field operators. Their contribution the Green function is found to restore the cluster property by cancelling, at large impact parameter, the constant term provided by the second ground state present in the ordered phase. For the impact parameter | B| < 2 √ α′ μ log s the Green function tends to a constant providing therefore for D = 1, the expanding disc behaviour which is consistent with s-channel unitary.