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

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

2010-12-15

arxiv.org/abs/1012.3263v2

Class. Quantum Grav. 28 (2011) 195018

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, no figure. v2: some calculation details removed to make the paper more concise (see v1 for the longer version), mino

Scientific paper

10.1088/0264-9381/28/19/195018

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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