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 ε(q, ω) obeys the Kramers-Kronig relations only when momentum q is identically equal to zero. For an arbitrary momentum q≠0 the dielectric function does not obey the Kramers-Kronig relations, and the static dielectric function at q≠0 may have a negative sign [ε(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 ε(q, 0)<0 at q≠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.