Non-Abelian Chern-Simons Particles and their Quantization

Abstract

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 non--trivial boundary conditions. Also, the equation is compared with the one given in the literature.

18 pages, MIT preprint CTP # 2276

References in corpus (7)

• Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance
• Non-abelian vortices and non-abelian statistics
• Perturbative Bosonic End Anyon Spectra and Contact Interactions
• Chern-Simons Solitons, Toda Theories and the Chiral Model
• Differential Regularization of a Non-relativistic Anyon Model
• Finite and Infinite Symmetries in (2+1)-Dimensional Field Theory
• Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles

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• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Schroedinger Self-adjoint Extension and Quantum Field Theory
• Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering
• High-temperature QCD and the classical Boltzmann equation in curved spacetime
• Noncommuting fields and non-Abelian fluids
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• Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
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• Classical and Quantum Mechanics of Non-Abelian Chern-Simons Particles
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• Nonrelativistic Supersymmetry in Noncommutative Space
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• Gauged Nonlinear Sigma Model and Boundary Diffeomorphism Algebra
• On the Nonabelian Aharonov Bohm Scattering of Spinless Particles
• Spontaneous Symmetry Breaking in the Non-Abelian Anyon Fluid
• Radiation Damping of a BPS Monopole; an Implication to S-duality
• Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction I: plasmon -- hard particle scattering
• Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons
• Exchange and exclusion in the non-abelian anyon gas
• Semiclassical Theory for Two-anyon System
• The gauge coupled two-body problem in a ring
• Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory
• New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: Classical and Quantal Analysis
• Almost critical regularity of non-abelian Chern-Simons-Higgs system in the Lorenz gauge