The dispersion theory of dispersion forces

The long-range forces that act between neutral atoms and molecules have been known as dispersion forces since the work of London, who was the first to make manifest the connection between these forces and the dispersion of light by atoms, already guessed at by Newton. The analysis and application of the analyticity properties of scattering amplitudes, developed several decades ago in the context of quantum field theory, is known as dispersion theory. In this article we review the approach to dispersion forces based on dispersion theory. We give a general discussion of the concept of potential in quantum field theory and then show how a study of two-photon exchange amplitudes leads to a model-independent derivation and generalization of the formulas describing retarded dispersion forces for the case of two neutral atoms, first obtained by Casimir and Polder. We then review later extentions to the interaction of a charged and a neutral system and recent work on the case where both systems are charged. The connection between the dispersion-theory approach and more conventional methods is described. We also illustrate the use of dispersion-theory techniques to study forces arising from two-neutrino exchange and two-meson exchange. The effect of dispersion forces on the energy levels of the Rydberg states of hilium is briefly sketched. Finally, some open questions are mentioned.