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Infrared divergences from the exchange of dynamically screened magneticgluons (photons) lead to the breakdown of the Fermi liquid description of the{\em normal} state of cold and dense QCD and QED. We implement a resummation ofthese divergences via the renormalization group to obtain the spectral density,dispersion relation, widths and wave function renormalization of singlequasiparticles near the Fermi surface. We find that all feature scaling withanomalous dimensions:  $\omega_p({k}) \propto |k-k_F|^{\frac{1}{1-2\lambda}} ~ ; ~ \Gamma(k) \propto|k-k_F|^{\frac{1}{1-2\lambda}} ~;~ Z_p({k}) \propto|k-k_F|^{\frac{2\lambda}{1-2\lambda}}$ with $\lambda = \frac{\alpha}{6\pi} ~{for QED} \vspace{0.5 ex} ~,~ \frac{\alpha_s}{6\pi} \frac{N^2_c-1}{2N_c}\~~{for QCD with}$. The discontinuity of the distribution function forquasiparticles near the Fermi surface vanishes. The dynamical renormalizationgroup is implemented to study the relaxation of quasiparticles in real time.Quasiparticles with Fermi momentum have vanishing group velocity and relax witha power law with a coupling dependent anomalous dimension.Comment: 39 pages, 2 figure

Non-Fermi-liquid aspects of cold and dense QED and QCD: Equilibrium and nonequilibrium