Reddit mentions of Solid State Physics

It comes out when you derive the dielectric function as a correlation function in many-body pertubation theory in a Bloch basis. You will in general get an infinite series of Feynman diagrams corresponding to virtual particle-hole pair interactions.

In the Random Phase Approximation for an electron gas the dielectric function is the Lindhard function, which as you can see has a sum over electron-hole pairs. The slightly more realistic and complicated expression in the case of transverse polarized fields and crystalline solid is in many books on solid state physics, e.g. http://www.amazon.com/Solid-Physics-Second-Giuseppe-Grosso/dp/0123850304/ref=sr_1_9?s=books&ie=UTF8&qid=1449329113&sr=1-9&keywords=solid+state+physics

The equation is basically the overlap of the dipole of all particle-hole pairs with the EM wave weighted by 1/(E-hω), where E is the energy of the particle-hole pair. So even though hω is not exactly equal to or that close to any E, there is still a considerable contribution to the dielectric function. Even in the classical electrodynamical picture the electrons move when the EM wave moves through the solid and generate small oscillating charge displacements.

So to conclude: Normally electron-hole pairs are considered static solutions when no field is present. The light-matter photons/polaritons are dynamical solutions when an external field is present and can be approximated by an infinite series in the static solutions.