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

TL;DR

This paper quantizes abelian Chern-Simons theory on a torus, deriving an effective Hamiltonian and many-anyon Schrödinger equation with periodic potentials, offering new insights into anyon behavior without flux quantization.

Contribution

It introduces a novel quantization method for abelian Chern-Simons theory on a torus that avoids flux quantization and derives the periodic many-anyon Schrödinger equation.

Findings

Effective Hamiltonian with periodic matter fields

Derivation of many-anyon Schrödinger equation with periodic Aharonov-Bohm potentials

Analysis of wavefunction periodicity and comparison with previous approaches

Abstract

We quantize the abelian Chern-Simons theory coupled to non-relativistic matter field on a torus without invoking the flux quantization. Through a series of canonical transformations which is equivalent to solving the Gauss constraint, we obtain an effective hamiltonian density with periodic matter field. We also obtain the many-anyon Schr\"odinger equation with periodic Aharonov-Bohm potentials and analyze the periodic property of the wavefunction. Some comments are given on the different features of our approach from the previous ones.