Anyons on a Torus

TL;DR

This paper establishes a fundamental equivalence between anyon quantum mechanics on a torus and Chern-Simons gauge theory, clarifying the structure of their physical Hilbert space and operator commutation relations.

Contribution

It proves the equivalence between anyon quantum mechanics on a torus and Chern-Simons gauge theory, and analyzes operator commutation properties within the physical Hilbert space.

Findings

Proved the equivalence between anyon quantum mechanics on a torus and Chern-Simons gauge theory.

Showed that Hamiltonian and total momenta commute only in the physical Hilbert space.

Clarified the operator algebra structure in the physical Hilbert space.

Abstract

We prove the equivalence between anyon quantum mechanics on a torus and Chern-Simons gauge theory. It is also shown that the Hamiltonian and total momenta commute among themselves only in the physical Hilbert space.