  We construct the low energy theory of a doped Mott insulator, such as the
high-temperature superconductors, by explicitly integrating over the degrees of
freedom far away from the chemical potential. For either hole or electron
doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson
mediates dynamical spectral weight transfer across the Mott gap and creates a
new charge e excitation by binding a hole. The result is a bifurcation of the
electron dispersion below the chemical potential as observed recently in
angle-resolved photoemission on Pb-doped Bi_2Sr_2CaCu_2O_{8+\delta} (Pb2212).
