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

## TL;DR

This paper demonstrates that the production of pions in dynamic cascade models exhibits self-similarity and critical behavior, linking out-of-equilibrium processes to equilibrium phase transition properties through a specific mapping process.

## Contribution

It introduces a novel approach connecting dynamic cascade models with equilibrium phase transition features via a self-composition operator on a boson field.

## Key findings

- Self-similarity observed in pion production models
- Criticality associated with phase transition properties
- Mapping process links out-of-equilibrium dynamics to equilibrium phenomena

## Abstract

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

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Source: https://tomesphere.com/paper/1905.00326