  The dispersion relation of a doped hole in the half-filled 2D Hubbard model
is shown to follow a k^4 law around the (0,pi) and (pi,0) points in the
Brillouin zone. Upon addition of pair-hopping processes this dispersion
relation is unstable towards a k^2 law. The above follows from T=0 Quantum
Monte calculations of the single particle spectral function A(k, omega) on 16 X
16 lattices. We discuss finite dopings and argue that the added term restores
coherence to charge dynamics and drives the system towards a d_x^2 - y^2
superconductor.
