Classical and Quantum Mechanics of Non-Abelian Chern-Simons Particles

Abstract

We investigate the classical and quantum properties of a system of $SU(N)$ non-Abelian Chern-Simons (NACS) particles. After a brief introduction to the subject of NACS particles, we first discuss about the symplectic structure of various $SU(N)$ coadjoint orbits which are the reduced phase space of $SU(N)$ internal degrees of freedom or isospins. A complete Dirac's constraint analysis is carried out on each orbit and the Dirac bracket relations among the isospin variables are calculated. Then, the spatial degrees of freedom and interaction with external gauge field are introduced by considering the total reduced phase space which is given by an associated bundle whose fiber is one of the coadjoint orbits. Finally, the theory is quantized by using the coherent state method and various quantum mechanical properties are discussed in this approach. In particular, a coherent state representation of the Knizhnik-Zamolodchikov equation is given and possible solutions in this representation are discussed.

28 pages, Revtex, revised version

References in corpus (7)

• Non-Abelian Chern-Simons Particles and their Quantization
• Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect
• Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles
• Non-Abelian Chern-Simons Quantum Mechanics
• Schrödinger Fields on the Plane with non-Abelian Chern-Simons Interactions
• Integrable Systems on Flag Manifold and Coherent State Path Integral
• Phase Space Structure of Non-Abelian Chern-Simons Particles

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• Large N Limit of Higher Derivative Extended CP(N) Model
• Canonical Quantization of Noncompact Spin System
• Multiple Solutions for the Non-Abelian Chern--Simons--Higgs Vortex Equations