  We consider a symmetric scalar theory with quartic coupling in 2- and
3-dimensions and compare the self-consistent 4-point vertex obtained from the
4PI effective action with the Bethe-Salpeter 4-vertex from 2PI effective
action. At zero external momenta the two vertices agree well with each other
when the coupling strength is small, but differences between them become more
and more pronounced as the coupling strength is increased. We also study the
momentum dependence of the two vertices and show that for certain momentum
configurations they are almost identical, but differ for general momentum
arguments.
