CONSERVING APPROXIMATIONS - ELECTRON-GAS WITH EXCHANGE EFFECTS

The conserving approximation includes a correct mix of the self-energy Sigma(p) and the vertex function Gamma(p,p + q). Only keeping the exchange self-energy Sigma(x)(p), we obtain the self-consistent equation for the vertex function Gamma(x)(p,p + q) in the closed form, which can be solved numerically. Using this vertex function, the polarization P-x(q) is obtained. We evaluate the long-wavelength limit of P-x(q) in the static case at both zero and nonzero temperatures. The latter case is compared with results obtained using the density-functional approach.