Abstract
The excitation energies in the random phase approximation with exchange can be found from the linearised equations of motion of electron-hole pairs. This is expressed in a real space representation in which many-body interactions and one-electron hopping are treated on the same footing. In the real space representation both the direct and exchange interactions between electron-hole pairs are included, so excitons, plasmons and single-particle excitations are all contained in the formalism. This is applied to a model insulator, first without one-electron hopping: this shows a dispersive Frenkel exciton and charge transfer excitations. When one-electron hopping is included, the Frenkel exciton can lie within the single-particle continuum; the charge transfer states become Wannier excitons. Applied to metals, the real space technique gives exactly the same plasmon frequency as the usual dielectric function method.