The CPT and Bisognano-Wichmann Theorems for Anyons and Plektons in d=2+1

TL;DR

This paper extends the Bisognano-Wichmann and CPT theorems to particles with braid group statistics in 2+1 dimensions, under assumptions of Poincare covariance and asymptotic completeness.

Contribution

It provides a rigorous proof of these fundamental theorems for anyons and plektons in three-dimensional quantum field theory.

Findings

Proves Bisognano-Wichmann theorem for braid group statistics

Establishes CPT invariance for particles with braid group statistics

Requires particles to have isolated, finitely degenerate mass spectra

Abstract

We prove the Bisognano-Wichmann and CPT theorems for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory, assuming Poincare covariance and asymptotic completeness. The particle masses must be isolated points in the mass spectra of the corresponding charged sectors, and may only be finitely degenerate.