Hausdorff dimension, fractional spin particles and Chern-Simons effective potential

TL;DR

This paper explores the Hausdorff dimension of fractional spin particles, links it to the Chern-Simons potential, and defines topological invariants based on particle statistics, advancing understanding of topological quantum properties.

Contribution

It introduces a general method to compute Hausdorff dimensions for fractional spin particles and connects these to Chern-Simons potentials and topological invariants.

Findings

Derived Hausdorff dimensions for particles of any spin

Established a connection between Hausdorff dimension and Chern-Simons potential

Defined topological invariants based on particle statistics

Abstract

We obtain for any spin, $s$, the Hausdorff dimension, $h_{i}$, for fractional spin particles and we discuss the connection between this number, $h_{i}$, and the Chern-Simons potential. We also define the topological invariants, $W_s$, in terms of the statistics of these particles.