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In this work we reveal that the inside-outside dynamic model for theproduction of fermion-antifermion pair (or quark-antiquark in QCD), is an outof equilibrium process. Properties of a complex system as the self-similarityand the critical point of a continuous phase transition in equilibrium appear.In this work we show that this is accomplished imposing a type of mappingprocess through a self-composition operator on a QED_2 bosons (or pions) field.

Self-Similarity and Criticality in the Boson (pions) field produced according to dynamic cascade models