  We construct a new functional for the single particle Green's function, which
is a variant of the standard Baym Kadanoff functional.
  The stability of the stationary solutions to the new functional is directly
related to aspects of the irreducible particle hole interaction through the
Bethe Salpeter equation.
  A startling aspect of this functional is that it allows a simple and rigorous
derivation of both the standard and extended dynamical mean field (DMFT)
equations as stationary conditions. Though the DMFT equations were formerly
obtained only in the limit of infinite lattice coordination, the new functional
described in the work, presents a way of directly extending DMFT to finite
dimensional systems, both on a lattice and in a continuum. Instabilities of the
stationary solution at the bifurcation point of the functional, signal the
appearance of a zero mode at the Mott transition which then couples t o
physical quantities resulting in divergences at the transition.
