A MODEL OF RELATIVISTIC ONE-COMPONENT PLASMA WITH DARWIN INTERACTIONS

We study a classical (non-quantum) model of relativistic one-component plasma described by the restricted Darwin-Breit Hamiltonian. In this model, two mobile charges interact via the familiar Coulomb potential plus a retarded electromagnetic potential of order 1/c(2) which mixes their positions and canonical momenta. The equilibrium distribution fu nctions of the infinite system can be formally represented by Mayer gr aph series in the canonical phase space of the particles. We proceed t o an exact reorganization of these series which remove short- and long -range divergencies arising from the 1/r-nature of both the Coulomb an d the 1/c(2) Darwin potentials. The method combines a perturbative tre atment of the relativistic interactions to resummations of convolution s chains analogous to that introduced in the purely Coulomb case. It l eads to a rather weak algebraic oscillatory autoscreening of the Darwi n interactions, while the Coulomb interactions are exponentially scree ned as usual. Our resummed diagrammatical representations provide rela tivistic corrections to the Coulomb quantities in a systematic way, be yond the previous mean-field estimations. We also briefly present a re lated model based on the full Darwin-Breit Hamiltonian which incorpora tes many-body interactions with arbitrary high orders in lie. We argue that, as far as the description of a weakly relativistic real plasma is concerned, the predictions of both models are equally questionable, even at the level of the mean-field approximation. The corresponding discussion requires the introduction of the theory of quantum electrod ynamics (QED) at finite temperature. Only this theory provides a compl ete and coherent treatment of the electromagnetic interactions which a re dropped out from the start in both model Hamiltonians, as detailed in a next paper. Here, we give the qualitative regimes of validity of the Darwin approach which are inferred from the QED analysis.