Fractal distribution function and fractal-deformed Heisenberg algebras

TL;DR

This paper introduces a fractal distribution function for fractons and derives a corresponding fractal-deformed Heisenberg algebra that incorporates braid group structures in two-dimensional spaces.

Contribution

It presents a novel fractal distribution function and a new algebraic framework for fractons, linking fractal geometry with quantum algebraic structures.

Findings

Derived a fractal distribution function for fractons

Constructed a fractal-deformed Heisenberg algebra

Connected braid group topology with quantum algebra

Abstract

We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account the braid group structure of these objects which live in two-dimensional multiply connected space.