Retarded transverse current-current response functions of a two-dimensional electron gas

The retarded transverse current-current response functions of an ideal two-dimensional electron gas at zero temperature are calculated. Introducing a new approximation scheme which allows one to take account of the reaction of the electromagnetic field to the induced current, i.e. the influence of the electronic induced current on the dynamics of the electromagnetic field, within the framework of the conventional linear response theory in a self-consistent way, a possible form of the dispersion relation for the transverse plasmon in the system is obtained. It is found that the energy of the transverse plasmon has a gap at k=0, if the thickness of the system is finite, in contrast to the longitudinal case.