Topological defects, fractals and the structure of quantum field theory

TL;DR

This paper explores the formation of topological defects in quantum field theory, the connection between fractals and coherent states, and how fractal properties emerge from local deformations within the mathematical framework of entire functions.

Contribution

It introduces a novel link between fractals and coherent states via q-deformed algebra, providing new insights into defect formation and fractal dynamics in quantum field theory.

Findings

Fractal structures are related to the formation of topological defects.

Coherent states exhibit fractal properties through q-deformation.

Fractal characteristics are integrated into the theory of entire functions.

Abstract

In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical structure of quantum field theory with particular reference to the processes of non-equilibrium symmetry breaking. The functional realization of fractals in terms of the q-deformed algebra of coherent states is also presented. From one side, this sheds some light on the dynamical formation of fractals. From the other side, it also exhibits the fractal nature of coherent states, thus opening new perspectives in the analysis of those phenomena where coherent states play a relevant role. The global nature of fractals appears to emerge from local deformation processes and fractal properties are incorporated in the framework of the theory of entire analytical functions.