Frequency dependence of the electron self-energy in a two-dimensional electron liquid

We have studied the effects of the electron-electron interaction on the frequency dependence of the quasiparticle self-energy of a two-dimensional electron gas. Our approach is patterned after Hedin's GW approximation. We find that many-body effects associated with charge and spin fluctuations induced vertex corrections are important and cannot be neglected. For the sake of illustration the calculations have been carried out at zero temperature and taking advantage of the plasma-pole scheme. The validity of the familiar on-shell approximation is discussed.