Anyonic physical observables and spin phase transition

TL;DR

This paper investigates the quantization of charged matter coupled to Chern-Simons gauge fields, constructs gauge-invariant anyon operators, and explores how a spin phase transition via the Higgs mechanism transforms anyons into bosons or photons.

Contribution

It introduces a covariant gauge fixing approach to identify physical anyon operators and analyzes the spin phase transition's effect on fractional statistics.

Findings

Constructed gauge-invariant physical anyon operators.

Demonstrated the Higgs mechanism transmuting anyons into bosons or photons.

Provided a method to identify physical spectra free from gauge ambiguity.

Abstract

The quantization of charged matter system coupled to Chern-Simons gauge fields is analyzed in a covariant gauge fixing, and gauge invariant physical anyon operators satisfying fractional statistics are constructed in a symmetric phase, based on Dirac's recipe performed on QED. This method provides us a definite way of identifying physical spectrums free from gauge ambiguity and constructing physical anyon operators under a covariant gauge fixing. We then analyze the statistical spin phase transition in a symmetry-broken phase and show that the Higgs mechanism transmutes an anyon satisfying fractional statistics into a canonical boson, a spin 0 Higgs boson or a topologically massive photon.