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The self-consistent theory for obtaining the spin-dependent local-field correction G ± (q) due to Singwi, Tosi, Land and Sjölander is extended to investigate the exchange and correlation effects in the three-dimensional electron gas in strong magnetic fields. We find that G ± (q) barely changes with H as long as it is weak enough for the ratio of , the magnetic length, to r 0 , the average interelectron spacing, to be larger than about 0.7. With this information, we calculate the self-energy in a self-consistent way to obtain the electronic structure of graphite in strong magnetic fields. The result obtained is in agreement with experiment.

The spin-charge-orbital complex structures of manganites are studied using topological concepts. The key quantity is the "winding number" w associated with the Berry-phase connection of an e(g) electron parallel transported through Jahn-Teller centers, along zigzag one-dimensional paths in an antiferromagnetic environment of t(2g) spins. From these concepts, it is shown that the "bi-stripe" and "Wigner-crystal" states observed experimentally have different w's. Predictions for the spin structure of the charge-ordered states for heavily doped manganites are discussed.

Based on the Bethe-Salpeter equation and the Ward identity derived from it, we provide a scheme for constructing the vertex function in the self-consistent iteration loop to determine the electron self-energy. The scheme is implemented in the homogeneous electron gas at the sodium density.

We develop a scheme for building the scalar exchange-correlation ͑XC͒ kernel of time-dependent density functional theory ͑TDDFT͒ from the tensorial kernel of time-dependent current density functional theory ͑TDCDFT͒ and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation ͑LDA͒ to TDDFT. As an application of this general scheme, we calculate the dynamical XC contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.

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