  Starting from the (Hubbard) model of an atom, we demonstrate that the
uniqueness of the mapping from the interacting to the noninteracting Green's
function, $G\to G_0$, is strongly violated, by providing numerous explicit
examples of different $G_0$ leading to the same physical $G$. We argue that
there are indeed infinitely many such $G_0$, with numerous crossings with the
physical solution. We show that this rich functional structure is directly
related to the divergence of certain classes of (irreducible vertex) diagrams,
with important consequences for traditional many-body physics based on
diagrammatic expansions. Physically, we ascribe the onset of these highly
non-perturbative manifestations to the progressive suppression of the charge
susceptibility induced by the formation of local magnetic moments and/or RVB
states in strongly correlated electron systems.
