In conventional Green's function methods the vertex function Gamma is
generally energy dependent. However, a model-space Green's function me
thod where the vertex function is manifestly energy independent can be
formulated using energy-independent effective interaction theories ba
sed on folded diagrams and/or similarity transformations. This is disc
ussed in general and then illustrated for a 1p1h model-space Green's f
unction applied to a solvable Lipkin many-fermion model. The poles of
the conventional Green's function are obtained by solving a self-consi
stent Dyson equation and model space calculations may lead to unphysic
al poles. For the energy-independent model-space Green's function only
the physical poles of the model problem are reproduced and are in sat
isfactory agreement with the exact excitation energies.