We evaluate the ground-state properties of a charged Bose gas at
T=0 within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj\"olander. The dynamical nature of the local- field correction is retained to include dynamic correlation effects. The resulting static structure factor
S(q) and the local-field factor
G(q) exhibit properties not described by other mean-field theories.
We study the correlation effects in a one-dimensional Bose gas with repulsive delta-function interaction. The correlation effects are described by a local-field correction which takes into account the short-range correlations. We find that the ground state energy is in good agreement with the exact result up to intermediate coupling strengths, showing an improvement over the Bogoliubov and other related approximations. The velocity of sound, the static structure factor, and pair-correlation function are also calculated within the present approximation.
Some properties of a two-dimensional charged Bose gas interacting with a ln(r) potential are investigated on the basis of a self-consistent-field formalism which includes the short-range correlations between bosons through a local-field correction depending on the pair correlation function. Numerical results for the static structure factor, pair correlation function, spectrum of elementary excitations, and the response of the system to a static impurity charge are presented. Our results show the same qualitative behavior as those of the three-dimensional analog but the correlation effects are somewhat more pronounced in two dimensions.