On an admissible sign of the static dielectric function of matter

This paper is a review of the present status of the problem of the properties of the dielectric function of matter. It is shown that the dielectric function $\ensuremath{\epsilon}(\mathrm{q}, \ensuremath{\omega})$ obeys the Kramers-Kronig relations only when momentum q is identically equal to zero. For an arbitrary momentum $\mathrm{q}\ensuremath{\ne}0$ the dielectric function does not obey the Kramers-Kronig relations, and the static dielectric function at $\mathrm{q}\ensuremath{\ne}0$ may have a negative sign [$\ensuremath{\epsilon}(\mathrm{q}, 0)<0$]. It is shown that the appearance of a negative sign for the static dielectric function does not contradict the requirements of system stability. Special attention is paid to the possible existence of a negative sign for the static dielectric function in real physical systems. It is shown that the inequality $\ensuremath{\epsilon}(\mathrm{q}, 0)<0$ at $\mathrm{q}\ensuremath{\ne}0$ is valid for a rather wide class of condensed media (simple metals, nonideal plasma, etc.). The interrelation between the existence of a negative sign for the dielectric function and the problem of high-temperature superconductivity is briefly discussed.