Dielectric Formulation of Quantum Statistics of Interacting Particles

Formal relations between the free energy, the "dielectric constant" which expresses the response of the system to an external perturbation, and the two-particle Green's function in temperature space are derived. Connection with perturbation expansion for free energy and for general admittance tensors are established. These results are applied to a general discussion of the random-phase approximation at finite temperature and it is shown that the sum of ring diagrams corresponds to the calculation of the dielectric constant in the approximation of the neglect of local field corrections.