Self-consistent mean field theories

The author points out that there is a variety of mean field theories which are also self-consistent, according to differing criteria. This discussion uses the phrase ''self-consistent mean field'' in a narrowly defined sense. To define this sense systems are considered that interact among themselves. A supreme example of a self-consistent mean field theory is a set of Maxwell-Bloch equations describing the coupling of N identical two-level atoms to a coherent radiation field. A second example comes from nuclear physics and is related to the deep inelastic collisions of heavy ions. These experiments were undertaken with the hope of obtaining superheavy nuclei. A third example comes from astrophysics and concerns the problem of stellar dynamics. The final example concerns the spectrum and the optical interactions of atoms injected into an interacting medium. The author points out the similarities between the self-consistent mean field theory and the method of density functional formalism which is used in the impurity problem in charged liquids