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arXiv · 1012.3263

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

M. Ciafaloni·S. Munier
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Abstract

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.

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M. Ciafaloni, S. Munier. 2011-09-15. Hamiltonian solutions of the 3-body problem in (2+1)-gravity. https://doi.org/10.1088/0264-9381%2F28%2F19%2F195018

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