Long-wavelength description of multicomponent neutral and Coulomb systems: response functions, identies for Green's functions and equilibrium conditions

The generalization of the Ward-Pitaevskii identity for many-particle systems with a potential of interparticle interaction, which is a sum of short-range and Coulomb parts, is obtained. The relations between this identity and the long-wavelength limit of density- density response functions and polarization functions are determined. Concrete expressions for these functions in this limit are also found from the thermodynamic derivatives. It is shown that the generalization of the Ward-Pitaevskii identity leads to a modification of the thermodynamical equilibrium condition for a system in an external field.