SEZIONE DI ROMA I
The problem of N particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some remarkable specific cases have been solved in one dimension. Here we show that the guiding center approximation---valid for charges moving in two dimensions in the limit of large constant magnetic fields---simplifies the three-body problem for an arbitrary interparticle interaction invariant under rotations and translations, making it solvable by quadratures.
A spinorial representation for the system is introduced, which allows a visualization of its phase space as the corresponding Bloch sphere. Finally, a discussion of the quantization of the problem is presented.
Francois Leyvraz (Instituto de Fisica, Universidad Nacional Autonoma de Mexico)