Fractal statistics, fractal index and fractons
Wellington da Cruz

TL;DR
This paper introduces the concept of fractal index and explores the properties of fractons, particles obeying fractal statistics, linking them to conformal field theory, Hausdorff dimension, and number theory.
Contribution
It establishes a novel connection between fractal statistics, conformal field theory, and number theory through the fractal index and Hausdorff dimension.
Findings
Relation between fractons and CFT-quasiparticles
Connection between Hausdorff dimension and conformal anomaly
Link between Rogers dilogarithm, Farey series, and fractal index
Abstract
The concept of fractal index is introduced in connection with the idea of universal class of particles or quasiparticles, termed fractons, which obey fractal statistics. We show the relation between fractons and conformal field theory(CFT)-quasiparticles taking into account the central charge and the particle-hole duality , for integer-value of the statistical parameter. The Hausdorff dimension which labelled the universal classes of particles and the conformal anomaly are therefore related. We also establish a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Theoretical and Computational Physics · Mathematical Dynamics and Fractals
