Fractional Statistics: Quantum Possibilities in Two Dimensions

Abstract

A standard notion of quantum mechanics is that all particles, elementary or composite, must fall into one of two fundamental categories: fermions or bosons. However, it has recently been discovered that there can be quantum particles which are neither fermions nor bosons. Such particles (anyons) can only occur in two spatial dimensions-yet this does not rule out their existence, for they are found as elementary excitations in confined, quasi-two-dimensional condensed-matter systems and may occur in other systems as well. An overview of the argument for the existence of anyons is presented, along with a discussion of their role in condensed-matter physics.