  We analyze quantum fluctuation effects at the onset of charge or spin density
wave order in two-dimensional metals with an incommensurate nesting ($2k_F$)
wave vector connecting two pairs of hot spots on the Fermi surface. We first
compute the momentum and frequency dependence of the fermion self-energy near
the hot spots to leading order in a perturbation expansion (one loop).
Non-Fermi liquid behavior with a linear (in energy) quasi-particle decay rate
and a logarithmically vanishing quasi-particle weight is obtained. The momentum
dependence of the self-energy entails only finite renormalizations of the Fermi
velocity and the Fermi surface curvature at the hot spots. The perturbative
one-loop result is not self-consistent and casts doubt on the stability of the
$2k_F$ quantum critical point. We construct a self-consistent solution of the
one-loop equations with self-energy feedback, where the quantum critical point
is stabilized rather than being destroyed by fluctuations, while the non-Fermi
liquid behavior as found in the perturbative one-loop calculation is confirmed.
