|Location:||MSRI: Simons Auditorium|
The N-body problem in d-dimension space has symmetry group SE(d).
Centre of mass reduction leads to a system with SO(d) symmetry acting
diagonally on positions and momenta. For N=3, d=4 reduction of the SO(4)
symmetry is complicated because the tensor of inertia is non-invertible.
The fully reduced system has 4 degrees of freedom and a Hamiltonian that
is not polynomial in the momenta. The most surprising property of the
reduced Hamiltonian is that it has equilibria that are minima.