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arXiv · hep-th/0008222

Fractal statistics, fractal index and fractons

Wellington da Cruz
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Abstract

The concept of fractal index is introduced in connection with the idea of universal class $h$ 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 $c[ν]$ and the particle-hole duality $ν\longleftrightarrow\frac{1}ν$, for integer-value $ν$ of the statistical parameter. The Hausdorff dimension $h$ 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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Wellington da Cruz. 2000-10-10. Fractal statistics, fractal index and fractons. https://doi.org/10.1142/9789812810366_0007

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