On the 'toy model" in the Reggeon field theory

The Reggeon field theory with zero transverse dimensions is studied in the Hamiltonian formulation for both sub-and supercritical pomeron. Mathematical aspects of the model, in particular the scalar products in the space of quantum states, are discussed. Relation to reaction-diffusion processes is derived in absence of pomeron merging. Numerical calculations for different parameters of the models, $\alpha(0)-1=\mu$ and the triple pomeron coupling constant $\lambda$, show that the triple pomeron interaction always makes amplitudes fall with rapidity irrespective of the value of the intercept. The smaller the values of the ratio $\lambda/\mu$ the higher are rapidities $y$ at which this fall starts, so that at small values of $\lambda$ it begins at asymptotically high rapidities (for $\lambda/\mu<1/4$ the fall is noticeable only at $\mu y>100$). No visible singularity is seen for the critical pomeron. A perturbative treatment is proposed which may be useful for more realistic models.