Abelian Chern-Simons field theory and anyon equation on a cylinder

TL;DR

This paper derives the anyon equation on a cylindrical geometry within abelian Chern-Simons theory, providing insights into the effective Hamiltonian and periodic properties relevant for condensed matter physics.

Contribution

It extends the abelian Chern-Simons framework to cylindrical geometries, deriving the effective Hamiltonian and analyzing periodic properties for the first time.

Findings

Derived the effective Hamiltonian for anyons on a cylinder

Established the periodic boundary conditions in cylindrical geometry

Extended the theory from plane and torus to cylinder

Abstract

We present the anyon equation on a cylinder and in an infinite potential wall from the abelian Chern-Simons theory coupled to non-relativistic matter field by obtaining the effective hamiltonian through the canonical transformation method used for the theory on a plane and on a torus. We also give the periodic property of the theory on the cylinder.