Fractal statistics, fractal index and fractons

Details Fractal statistics, fractal index and fractons Fractal statistics, fractal index and fractons

2000-08-29

arxiv.org/abs/hep-th/0008222v3

Geometrical Aspects of Quantum Fields, ed. by, A. A. Bytsenko, A. E. Gol\c{c}alves and B. M. Pimentel (World Scientific, 2001)

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 7 pages, references update, To appear Proceedings Workshop on Geometrical Aspects Of Quantum Fields, 17 to 22 April 200

Scientific paper

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 $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ 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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