Anyons in the Operational Formalism

TL;DR

This paper demonstrates that anyonic behavior in two-dimensional quantum systems arises from topology and is compatible with the operational formalism, extending the foundational understanding of particle statistics beyond fermions and bosons.

Contribution

It shows that anyons can be explained within the operational formalism, linking topology to particle statistics without requiring particles to be identical.

Findings

Anyons result from the topology of two-dimensional space.

Operational formalism can accommodate anyonic behavior.

Identical particles can exhibit anyonic statistics in 2D.

Abstract

The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4,5]. However, this seems to run counter to results in two-dimensional systems, which allow for anyons, particles with statistics which interpolate between Fermi-Dirac and Bose-Einstein (see [6] for a review). In this talk we will show that the results in two dimensions can be made compatible with the operational results. That is, we will show that anyonic behavior is a result of the topology of the space in two dimensions [7], and does not depend on the particles being identical; but that nevertheless, if the particles are identical, the resulting system is still anyonic.