Quantum statistics of coulomb systems: Thermodynamic functions and phase transitions

Matter is considered as a quantum system of nonrelativistic point charges, the electrons and the nuclei (or other positive particles). After the discussion of several exact bounds and stability theorems the low and high density structures of the thermodynamic functions (corresponding to ideal gases) are given. The corner of correlations in the density-temperature plane is treated by means of thermodynamic Green functions. The realistic description of correlations requires partial summations corresponding to the effects of screening (chains), bound states (ladders) and chemical equilibria (quasi-particle summations). It is shown that Coulomb interactions may cause thermodynamics instabilities corresponding to the first order plasma phase transitions.