  We generalize the numerical renormalization group scheme to study the
phonon-mediated retarded interactions in the high Tc cuprates. We find that
three sets of phonon-mediated retarded quasiparticle scatterings grow under RG
flow. These scatterings share the following common features: 1) the initial and
final quasiparticle momenta are in the antinodal regions, and 2) the scattering
amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction
are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$.
After growing strong, these retarded interaction will trigger density wave
orders with d-wave symmetry. However, due to the d-wave form factor they will
leave the nodal quasiparticle unaffected. We conclude that the main effect of
electron-phonon coupling in the cuprates is to promote these density wave
orders.
