Non-Abelian Chern-Simons particles and their quantization

A many-body Schrödinger 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 Schrödinger equation for the particles is obtained from both starting points. It is shown that the resulting interaction between particles can be replaced by nontrivial boundary conditions. Also, the equation is compared with the one given in the literature.