Pomeron calculus in zero transverse dimensions: Summation of pomeron loops and generating functional for multiparticle production processes

In this paper we address two problems in pomeron calculus in zero transverse dimensions: the summation of the pomeron loops and the calculation of the processes of multiparticle generation. We introduce a new generating functional for these processes and obtain the evolution equation for it. We argue that in the kinematic range given by 1 ≪ In (1/α_s ²) ≪ α_sY ≪ 1/αs, we can reduce the pomeron calculus to the exchange of non-interacting pomerons with the renormalized amplitude of their interaction with the target. Therefore, the summation of the pomeron loops can be performed using the Mueller-Patel-Salam- Iancu approximation.