Abstract
By defining the longitudinal and transverse frequencies in terms of the frequency moments of the response functions, the Lyddane-Sachs-Teller (LST) relation for electron liquids is derived from the Kramers-Kronig relations. The extension of the LST relation for finite wave numbers is possible if the dielectric function obeys the Kramers-Kronig relations at finite wave numbers. It is pointed out that the LST relation in principle allows one to experimentally check the validity of the Kramers-Kronig relations for the dielectric function at finite wave numbers.
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