  Electronic correlated systems are often well described by dynamical mean
field theory (DMFT). While DMFT studies have mainly focused hitherto on
one-particle properties, valuable information is also enclosed into local
two-particle Green's functions and vertices. They represent the main ingredient
to compute momentum-dependent response functions at the DMFT level and to treat
non-local spatial correlations at all length scales by means of diagrammatic
extensions of DMFT. The aim of this paper is to present a DMFT analysis of the
local reducible and irreducible two-particle vertex functions for the Hubbard
model in the context of an unified diagrammatic formalism. An interpretation of
the observed frequency structures is also given in terms of perturbation
theory, of the comparison with the atomic limit, and of the mapping onto the
attractive Hubbard model.
