Equilibrium long-ranged charge correlations at the surface of a conductor coupled to the electromagnetic radiation II

Results of a previous article with the same title are retrieved by a different method. A one-component plasma is bounded by a plane surface. The plasma is fully coupled to the electromagnetic field, therefore the charge correlations are retarded. The quantum correlation function of the surface charge densities, at times different by $t$, at asymptotical large distances $R$, at inverse temperature $\beta$, decays as $-1/(8\pi^2\beta R^3)$, a surprisingly simple result: the decay is independent of Planck's constant $\hbar$ and of the time difference $t$. The present paper is based on the analysis of the collective vibration modes of the system.