Non-Abelian Chern-Simons Particles and their Quantization

TL;DR

This paper derives and compares the many-body Schr"odinger equation for non-Abelian Chern--Simons particles from both particle and field perspectives, highlighting boundary conditions and quantization methods.

Contribution

It provides a unified derivation of the N-body Schr"odinger equation for non-Abelian Chern--Simons particles from multiple approaches, emphasizing boundary conditions and quantization.

Findings

Interaction replaced by boundary conditions

Derived N-body Schr"odinger equation from two perspectives

Compared with existing literature equations

Abstract

A many--body Schr\"odinger equation for non--Abelian Chern--Simons particles is obtained from both point--particle and field--theoretic pictures. We present a particle Lagrangian and a field theoretic Lagrange density, and discuss their properties. Both are quantized by the symplectic method of Hamiltonian reduction. An $N$--body Schr\"odinger equation for the particles is obtained from both starting points. It is shown that the resulting interaction between particles can be replaced by non--trivial boundary conditions. Also, the equation is compared with the one given in the literature.