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This paper concerns the equilibrium bulk charge and current densitycorrelation functions in quantum media, conductors and dielectrics, fullycoupled to the radiation (the retarded regime). A sequence of static andtime-dependent sum rules, which fix the values of certain moments of the chargeand current density correlation functions, is obtained by using Rytov'sfluctuational electrodynamics. A technique is developed to extract theclassical and purely quantum-mechanical parts of these sum rules. The sum rulesare critically tested in the classical limit and on the jellium model. Acomparison is made with microscopic approaches to systems of particlesinteracting through Coulomb forces only (the non-retarded regime). In contrastwith microscopic results, the current-current correlation function is found tobe integrable in space, in both classical and quantum regimes.

Charge and Current Sum Rules in Quantum Media Coupled to Radiation