Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles

TL;DR

This paper introduces a novel classical and quantum formulation of $SU(N+1)$ non-Abelian Chern-Simons particles using symplectic reduction and coherent state path integrals, extending understanding of these particles for any N.

Contribution

It develops a new classical formulation via symplectic reduction and quantizes $SU(N+1)$ NACS particles using BRST and coherent state methods, applicable for all N.

Findings

New classical formulation of $SU(N+1)$ NACS particles

Quantum model derived using BRST and coherent states

Applicable to arbitrary N in non-Abelian Chern-Simons theory

Abstract

We present a new method of formulating the classical theory of $SU(N+1)$ non-Abelian Chern-Simons (NACS) particles for arbitrary $N\geq 1$ using the symplectic reduction of $CP(N)$ manifold from $S^{2N+1}$. Quantizing the theory using BRST formulation and coherent state path integral method , we obtain a quantum mechanical model for $SU(N+1)$ NACS particles.