On the decoupling between classical Coulomb matter and radiation

We consider a model of matter coupled to radiation at equilibrium. Matter is described by a one-component plasma of classical point charges with Coulomb interactions, while radiation is represented by the classical transverse potential vector in Coulomb gauge. Using a straightforward generalization of the Bohr–van Leeuwen theorem, we show that the equilibrium properties of classical Coulomb matter remain unaffected by the presence of the classical radiation. As far as the real world is concerned, this decoupling does survive at large distances where both matter and radiation can be treated classically. This invalidates all the large-distances predictions, for the charge correlations, of the so-called Darwin models which incorporate retarded electromagnetic interactions beyond the instantaneous Coulomb potential. A second related important consequence is that the first relativistic corrections to the Coulomb thermodynamical quantities must be evaluated within the theory of quantum electrodynamics at finite temperature, even in a weakly relativistic and almost classical regime for matter.