  We further develop an extended dynamical mean field approach introduced
earlier. It goes beyond the standard $D=\infty$ dynamical mean field theory by
incorporating quantum fluctuations associated with intersite (RKKY-like)
interactions. This is achieved by scaling the intersite interactions to the
same power in 1/D as that for the kinetic terms. In this approach, a correlated
lattice problem is reduced to a single-impurity Anderson model with additional
self-consistent bosonic baths. Here, we formulate the approach in terms of
perturbation expansions. We show that the two-particle vertex functions are
momentum-dependent, while the single-particle self-energy remains local. In
spite of this, the approach is conserving. Finally, we also determine the form
of a momentum-dependent dynamical susceptibility; the resulting expression
relates it to the corresponding Weiss field, local correlation function and
(momentum-dependent) intersite coupling.
