  Several phenomenological self-energies have been presented to describe the
pseudogap in cuprates. Here, we offer a derivation of the self-energy in two
dimensions due to pair formation and compare it to photoemission data. We then
use our results to address several questions of interest, including the
existence of magneto-oscillations in the presence of the pseudogap, and the two
length scale nature of vortices in underdoped cuprates.
