ABSTRACT
This chapter provides a theoretical foundation for the linear-response formalism and the electrodynamic description of plasmas as continuous media. It introduces the linear response functions and outlines the fluctuation-dissipation theorem. The chapter establishes a rigorous description for the fluctuations and correlations in plasmas under thermodynamic equilibria. The dielectric response functions are a class of the linear response functions that emerge with the electrostatic approximation to the plasma, that is, when Coulomb interaction is assumed between the particles. The linear response functions are introduced in terms of the functional derivatives of physically observable quantities. In the theory of the many-particle system in thermodynamic equilibrium, the fluctuation-dissipation theorem provides a rigorous connection between the spectral functions of fluctuations and the imaginary parts of the relevant linear response functions. Finally the specific cases with the density-density response functions and the compressibility sum rules are treated in conjunction with the thermodynamic sum rules for the relaxation functions.
