Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect

Details Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm Effect

1993-12-20

arxiv.org/abs/hep-th/9312161v1

Annals Phys. 235 (1994) 413-434

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, Revtex 2.0, two figures available upon request, SNUTP-93/82

Scientific paper

10.1006/aphy.1994.1103

We construct a classical action for a system of $N$ point-like sources which carry SU(2) non-Abelian charges coupled to non-Abelian Chern-Simons gauge fields, and develop a quantum mechanics for them. Adopting the coherent state quantization and solving the Gauss' constraint in an appropriately chosen gauge, we obtain a quantum mechanical Hamiltonian given in terms of the Knizhnik-Zamolodchikov connection. Then we study the non-Abelian Aharonov-Bohm effect, employing the obtained Hamiltonian for two-particle sector. An explicit evaluation of the differential cross section for the non-Abelian Aharonov-Bohm scattering is given.

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