On the interaction of a charge with a thin plasma sheet

The interaction of the electromagnetic field with a two dimensional plasma sheet intended to describe the pi-electrons of a carbon nano-tube or a $C_{60}$ molecule is investigated. By integrating out first the displacement field of the plasma or first the electromagnetic field different representations for quantities like the Casimir energy are derived which are shown to be consistent with one another. Starting from the covariant gauge for the electromagnetic field it is shown that the matching conditions to which the presence of the plasma sheet can be reduced are different from the commonly used ones. The difference in the treatments does not show up in the Casimir force between two parallel sheets, but it is present in the Casimir-Polder force between a charge or a neutral atom and a sheet. At once, since the plasma sheet is a regularization of the conductor boundary conditions, this sheds light on the difference in physics found earlier in the realization of conductor boundary conditions as 'thin' or 'thick' boundary conditions in Phys.Rev.D70(2004)085010.