  Helium atom is the simplest many-body electronic system provided by nature.
The exact solution to the Schr\"odinger equation is known for helium ground and
excited states, and represents a workbench for any many-body methodology. Here,
we check the ab initio many-body GW approximation and Bethe-Salpeter equation
(BSE) against the exact solution for helium. Starting from Hartree-Fock, we
show that GW and BSE yield impressively accurate results on excitation energies
and oscillator strength, systematically improving time-dependent Hartree-Fock.
These findings suggest that the accuracy of BSE and GW approximations is not
significantly limited by self-interaction and self-screening problems even in
this few electron limit. We further discuss our results in comparison to those
obtained by time-dependent density-functional theory.
