Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect

TL;DR

This paper develops a quantum mechanical framework for non-Abelian Chern-Simons systems with point charges, revealing a non-Abelian Aharonov-Bohm effect with explicit scattering cross sections.

Contribution

It introduces a novel quantum mechanics for non-Abelian Chern-Simons sources using coherent state quantization and solves the Gauss constraint to derive the Hamiltonian.

Findings

Derived the Hamiltonian in terms of the Knizhnik-Zamolodchikov connection.

Analyzed the non-Abelian Aharonov-Bohm effect for two particles.

Provided explicit differential cross section for non-Abelian scattering.

Abstract

We construct a classical action for a system of $N$ point-like sources which carry SU(2) non-Abelian charges coupled to non-Abelian Chern-Simons gauge fields, and develop a quantum mechanics for them. Adopting the coherent state quantization and solving the Gauss' constraint in an appropriately chosen gauge, we obtain a quantum mechanical Hamiltonian given in terms of the Knizhnik-Zamolodchikov connection. Then we study the non-Abelian Aharonov-Bohm effect, employing the obtained Hamiltonian for two-particle sector. An explicit evaluation of the differential cross section for the non-Abelian Aharonov-Bohm scattering is given.