On the 'toy model" in the Reggeon field theory (original) (raw)

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, α(0) − 1 = µ and the triple pomeron coupling constant λ, 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 λ/µ the higher are rapidities y at which this fall starts, so that at small values of λ it begins at asymptotically high rapidities (for λ/µ < 1/4 the fall is noticeable only at µy > 100). No visible singularity is seen for the critical pomeron. A perturbative treatment is proposed which may be useful for more realistic models.