The exact solution of the many-body problem in one-point: insights in approximate Green's function approaches

In this work we obtain the exact one-body Green's function in one point by solving the Kadanoff-Baym equation. The result is a family of solutions. We show that only one of these solutions is a physical solution. We compare the exact physical solution to the exact solution of an approximate Kadanoff-Baym equation that was obtained recently [1] as well as to standard approximations such as GW. We show that the iterative solution of the GW equations is not always equal to the exact GW result. \\[4pt] [1] G. Lani, P. Romaniello and L. Reining, New J. Phys. 14, 013056 (2012)