Effect of the Lattice on the Internal Dielectric Constant

The properties of the dielectric constants, defined by using many-body theory, are considered. Especially, their dependence upon wave vectors is discussed. Internal dielectric constant for impurity potential in an insulator is shown to have no anomalous behavior at reciprocal lattice vectors. It is also shown that contribution to the dielectric constant from Umklapp terms vanishes at k =0.