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The study of quantum Coulomb systems at equilibrium is important forunderstanding properties of matter in many physical situations. Screening,recombination and van der Waals forces are basic phenomena which result fromthe interplay of Coulomb interactions, collective effects and quantummechanics. Those phenomena are introduced in the first part of this lecture,through various physical examples. Their treatment within mean-field theoriesand phenomenological approaches is also exposed, while related predictions arediscussed. This sheds light on fundamental issues, which must be analyzedwithout any \textsl{a priori} approximations or modelizations. The second partof this lecture is precisely devoted to the presentation of various exactresults for the quantum proton-electron hydrogen plasma. Such results arederived within the Screened Cluster Representation, which is constructed bycombining the path integral representation of the Coulomb gas with Mayer-likediagrammatical techniques. They illustrate the breakdown of Debye exponentialscreening by quantum fluctuations, as well as the emergence of familiarchemical species in suitable low-temperature and low-density limits. Also, theamplitude of van der Waals forces is shown to be reduced by free charges.

Quantum Coulomb systems : screening, recombination and van der Waals forces