  This study is related to the fluctuation theory of electromagnetic fields,
charges and currents. The three-dimensional system under consideration is a
semi-infinite conductor, modeled by the jellium, in vacuum. In previous
theoretical studies it was found that the correlation functions of the surface
charge density on the conductor decay as the inverse cube of the distance at
asymptotically large distances. The prefactor to this asymptotic decay was
obtained in the classical limit and in the quantum case without retardation
effects. To describe the retarded regime, we study a more general problem of
the semi-infinite jellium in thermal equilibrium with the radiated
electromagnetic field. By using Rytov's fluctuational electrodynamics we show
that, for both static and time-dependent surface charge correlation functions,
the inclusion of retardation effects causes the quantum prefactor to take its
universal static classical form, for any temperature.
