  We develop a Maxwell-Schroedinger formalism in order to describe the
radiative interaction mechanism between semiconductor quantum dots. We solve
the Maxwell equations for the electromagnetic field coupled to the polarization
field of a quantum dot ensemble through a linear non-local susceptibility and
compute the polariton resonances of the system. The radiative coupling,
mediated by both radiative and surface photon modes, causes the emergence of
collective modes whose lifetimes are longer or shorter compared to the ones of
non-interacting dots. The magnitude of the coupling and the collective mode
energies depend on the detuning and on the mutual quantum dot distance. The
spatial range of this coupling mechanism is of the order of the wavelength.
This coupling should therefore be accounted for when considering quantum dots
as building blocks of integrated systems for quantum information processing.
