VIRIAL EXPANSIONS FOR QUANTUM PLASMAS - DIAGRAMMATIC RESUMMATIONS

We are studying the equilibrium properties of quantum Coulomb fluids i n the low-density limit. In the present paper, we only consider Maxwel l-Boltzmann statistics. Use of the Feynman-Kac path-integral represent ation leads to the introduction of an equivalent classical system made of filaments interacting via two-body forces. All the corresponding M ayer-like graphs diverge because of the long-range Coulombic nature of the filament-filament potential. Inspired by the work of Meeron [J. C hem. Phys. 28, 630 (1958); Plasma Physics (McGraw-Hill, New York, 1961 )] for purely classical systems, we show that these long-range diverge ncies can be resummed in a systematic way. We then obtain a formal dia grammatic representation for the particle correlations of the genuine quantum system. The prototype graphs in these series are made of root and internal filaments, connected by two-body resummed bonds according to well-defined topological rules. The resummed bonds depend on the p article densities and decay faster than the bare Coulomb potential bec ause of screening. Some bonds decay algebraically as 1/r3 in accord wi th the absence of exponential clustering, while the other ones are sho rt ranged. This ensures the integrability of all the above prototype g raphs. Moreover, we show that the filament densities, which are the st atistical weights of the filaments in these graphs, can themselves be calculated in terms of the particle densities via a well-behaved diagr ammatic series. This provides a useful algorithm for expanding the Max well-Boltzmann thermodynamic functions in powers of the particle densi ties, as to be described in a second future paper. The exchange effect s due to Fermi or Bose statistics will be considered in a third paper.