A quantum-geometrical description of fracton statistics

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational values of spin. This formulation can be considered in the context of the fractional quantum Hall effect-FQHE and number theory. keywords: Fractal distribution function; fractal von Neumann entropy; fractional quantum Hall effect. Talk given at the 2nd International Londrina Winter School: Mathematical Methods in Physics, August, 26-30 (2002), Universidade Estadual de Londrina, Paraná, Brazil.