Quantum Coulomb systems: some exact results in the atomic limit

We review a number of exact results concerning the recombined electron–proton gas. The recombination problem can be formulated in precise terms in the atomic limit. In this limit one lets the density and the temperature tend to zero in a coupled way so that the resulting energy–entropy balance favors the formation of certain chemical species. This enables to develop a clear understanding of the dielectric versus conducting behavior in the system. In particular, we give a first principle derivation of the dielectric constant of the dilute atomic gas without presupposing the existence of atoms. The analysis relies on the path integral representation of the Coulomb gas together with Mayer diagrammatic techniques.