Engendering self-similarity in Boson field by a natural feedback process

In this work we suggest that the production of bosons (mesons) in a cascade process such as the one provided by the Schwinger and Bjorken models for the quark confinement, can be considered as a natural feedback process. Within this feedback process, a recurrent operator acts on the initial boson field function, which is mathematically expressed by some type of the zero-order Bessel function. The result of this recurrent operation is a temporal sequence of field structures that demonstrates the property of self-similarity. Each structure is part of the boson field function that results after a number of as many iterations as the structures that appear.