  We investigate the nonlinear interaction between a relativistically strong
laser beam and a plasma in the quantum regime. The collective behavior of the
electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled
with the electromagnetic wave through the Maxwell and Poisson equations. This
allows us to study the nonlinear interaction between arbitrarily large
amplitude electromagnetic waves and a quantum plasma. We have used our system
of nonlinear equations to study theoretically the parametric instabilities
involving stimulated Raman scattering and modulational instabilities. A model
for quasi-steady state propagating electromagnetic wavepackets is also derived,
and which shows the possibility of localized solitary structures in the quantum
plasma. Numerical simulations demonstrate the collapse and acceleration of the
electrons in the nonlinear stage of the modulational instability, as well as
the possibility of wake-field acceleration of the electrons to relativistic
speeds by short laser pulses at nanometer length scales. The study has
importance for the nonlinear interaction between a super-intense X-ray laser
light and a solid-density plasma, where quantum effects are important.
