Topological Spin-Statistics Theorem for Strings

TL;DR

This paper extends a topological proof of the spin-statistics theorem from point particles to string loops in three dimensions, showing that such strings should be bosons and excluding nonabelian statistics.

Contribution

It generalizes the topological spin-statistics proof to string loops, establishing their bosonic nature under certain assumptions.

Findings

String loops are shown to be bosons.

Nonabelian statistics are excluded for string loops.

The proof does not rely on relativity or field theory.

Abstract

Recently, a topological proof of the spin-statistics Theorem has been proposed for a system of point particles which does not require relativity or field theory, but assumes the existence of antiparticles. We extend this proof to a system of string loops in three space dimensions and show that by assuming the existence of antistring loops, one can prove a spin-statistics theorem for these string loops. According to this theorem, all unparametrized strings(such as flux tubes in superconductors and cosmic strings ) should be quantized as bosons. Also, as in the point particle case, we find that the theorem excludes nonabelian statistics.