Central to QED is the description of electromagnetic forces in terms of the exchange of so-called virtual photons. Thus the electrostatic repulsion between two electrons can be thought of as due to virtual photons being emitted by one electron and absorbed by the other. The fact that nobody has ever detected a graviton is no surprise, because gravity is so much weaker than electromagnetism. It turns out that an exchange of single gravitons between point masses does indeed yield an expression for the gravitational field with its familiar inverse-square law. Problems set in, however, when more complicated processes involving many gravitons are examined.
Gravity differs crucially from electromagnetism inasmuch as the gravitational field is nonlinear.
This nonlinearity arises because the gravitational field possesses energy, and energy has mass, which gravitates. In quantum language, this implies that gravitons will interact with other gravitons, unlike photons, which interact only with electric charges and currents and not with other photons. In QED, such loops occur when an electron emits and reabsorbs its own photon. The resulting infinities are removed by a mathematical procedure that is known as renormalization. If this is done properly, sensible answers are obtained.