  This paper concerns the equilibrium bulk charge and current density
correlation functions in quantum media, conductors and dielectrics, fully
coupled to the radiation (the retarded regime). A sequence of static and
time-dependent sum rules, which fix the values of certain moments of the charge
and current density correlation functions, is obtained by using Rytov's
fluctuational electrodynamics. A technique is developed to extract the
classical and purely quantum-mechanical parts of these sum rules. The sum rules
are critically tested in the classical limit and on the jellium model. A
comparison is made with microscopic approaches to systems of particles
interacting through Coulomb forces only (the non-retarded regime). In contrast
with microscopic results, the current-current correlation function is found to
be integrable in space, in both classical and quantum regimes.
