Abstract
By a suitable choice of phase space variables, which is natural for the reduction of a two-body problem, we couple two sources to the Chern-Simons-Witten action and obtain the exact two-body Hamiltonian. For particles of (nearly) equal mass and of small momenta, the Hamiltonian reduces to that of 't Hooft. In the corresponding geometry, when viewed from a particular frame, the relative coordinate moves on a cone of deficit angle equal to the classical Hamiltonian.
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