Notes on the static dielectric response function in the density functional theory

We discuss several aspects of the dielectric response theory application to the density functional theory. This field has been an unceasing source of confusion during several decades. The most frequent reasons for this confusion are (a) uncritical tranfer of the results, especially regarding so-called local field corrections, obtained in many-body perturbation theory onto density functional theory, and (b) mixing up the statements true for the exact density functional theory with those applicable to the local density approximation only. In these notes we try to draw an appropriate lines between those theories. We also discuss a newly introduced (X. Gonze, Ph. Ghosez, and R.W. Godby, Phys. Rev. Lett., 74, 4035, 1995) "polarization+density functional" and show that within a given (e.g., local density) approximation to the exchange-correlation energy the Gonze et al approach is exactly equivalent to the conventional one.