The path integral for Chern-Simons quantum mechanics

TL;DR

This paper derives the path integral formulation for a system of particles interacting via a Chern-Simons gauge field, revealing effective interactions and Aharonov-Bohm phases, and discusses the spin-statistics relation.

Contribution

It provides a new derivation of the path integral for Chern-Simons quantum mechanics from the operator formalism, highlighting effective interactions and topological phases.

Findings

Effective interactions generate Aharonov-Bohm phases.

Path integral representation derived from operator formalism.

Discussion of spin-statistics relation in the system.

Abstract

The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears, generating the usual Aharonov-Bohm phases. The spin-statistics relation is also considered.