Electric-field correlation in quantum charged fluids coupled to the radiation field

In a recent paper [S. El Boustani, P. R. Buenzli, and P. A. Martin, Phys. Rev. E 73, 036113 (2006)] about quantum charges in equilibrium with radiation, among other things the asymptotic form of the electric-field correlation has been obtained by a microscopic calculation. It has been found that this correlation has a long-range algebraic decay of the form 1/r3 (except in the classical limit). The macroscopic approach, in the Course of Theoretical Physics of Landau and Lifshitz, gives no such decay. In this Brief Report we revisit and complete the macroscopic approach of Landau and Lifshitz and suggest that, perhaps, the use of a classical electromagnetic field by El Boustani was not justified.