  We formulate the dynamical mean field theory directly in the continuum. For a
given definition of the local Green's function, we show the existence of a
unique functional, whose stationary point gives the physical local Green's
function of the solid. We present the diagrammatic rules to calculate it
perturbatively in the interaction. Inspired by the success of dynamical mean
field calculations for model Hamiltonian systems, we present approximations to
the exact saddle point equations which may be used in the strong coupling
regime, by using mappings onto generalized quantum impurity models.
