Fractal statistics, fractal index and fractons

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 $c[\nu ]$ and the particle-hole duality $\nu ⟷\frac{1}{\nu }$, 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.

Latex, 7 pages, references update, To appear Proceedings Workshop on Geometrical Aspects Of Quantum Fields, 17 to 22 April 2000, State University of Londrina (Londrina, Parana, Brazil)