Fermi-liquid theory of electronic topological transitions and screening anomalies in metals

General expressions for the contributions of the Van Hove singularity (VHS) in the electron density of states to the thermodynamic potential $\ensuremath{\Omega}$ are obtained in the framework of a microscopic Fermi-liquid theory. The renormalization of the singularities in $\ensuremath{\Omega}$ connected with the Lifshitz electronic topological transition (ETT) is found. Screening anomalies due to virtual transitions between VHS and the Fermi level are considered. It is shown that, in contrast with the one-particle picture of ETT, the singularity in $\ensuremath{\Omega}$ turns out to be two sided for interacting electrons.