  We discuss the fermionic excitation spectra of the dense QCD and QED plasma
at zero temperature, and analyze the stability of the normal (perturbative)
ground state. The standard re-summed perturbation theory breaks down because
the infrared (IR) divergences show up in the spectra near the Fermi surface. We
employ the effective field theory approach and the renormalization group to
investigate the dynamics near the Fermi surface. Our results indicate that the
dense QCD and QED plasma are non-Fermi-liquids.
