The Spin-Statistics Theorem for Anyons and Plektons in d=2+1

TL;DR

This paper proves the spin-statistics theorem for particles with braid group statistics in 2+1 dimensions, based on fundamental principles of local relativistic quantum theory and minimal assumptions.

Contribution

It establishes the spin-statistics connection for anyons and plektons in 2+1D using a rigorous quantum field theoretic approach under minimal assumptions.

Findings

Proves the spin-statistics theorem for braid group statistics

Relies on local relativistic quantum theory principles

Requires only a mass gap and degeneracy restrictions

Abstract

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass spectrum of the corresponding charged sector, and a restriction on the degeneracy of the corresponding mass.