No-Go Theorem for ``Free'' Relativistic Anyons in d=2+1

TL;DR

This paper proves that in 2+1 dimensions, relativistic anyons cannot be modeled as free fields that only create single-particle states from the vacuum, highlighting fundamental limitations in their quantum field theoretic description.

Contribution

It establishes a no-go theorem demonstrating the impossibility of describing relativistic anyons as free fields in quantum field theory.

Findings

Relativistic anyons cannot be modeled as free fields.

The basic fields necessarily create multi-particle states.

Fundamental limitations exist in the free field description of anyons.

Abstract

We show that a quantum field theoretic model of anyons cannot be ``free'' in the (restrictive) sense that the basic fields create only one-particle states out of the vacuum.