  The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in
a symmetry broken phase is investigated in the present work. The model
considered consists of spinless fermions with repulsive interaction on a simple
cubic lattice. The investigated symmetry broken phase is the charge density
wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at
half-filling. The calculations are based on the high dimensional approach, i.e.
an expansion in the inverse dimension $1/d$ is used. The finite dimensionality
is accounted for by the inclusion of linear terms in $1/d$ and the true finite
dimensional DOS. Special care is paid to the setup of a conserving
approximation in the sense of Baym/Kadanoff without inconsistencies. The
resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the
non symmetry broken and in the symmetry broken phase (AB-CDW). The
dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in
the limit $T \to 0$ due to a subtle cancellation of diverging mobility and
vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap
induced by the symmetry breaking is clearly discernible. In addition, the
vertex corrections of order $1/d$ lead to an excitonic resonance lying within
the gap.
