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

We study equilibrium and nonequilibrium aspects of the normal state of cold and dense QCD and QED. The exchange of dynamically screened magnetic gluons (photons) leads to infrared singularities in the fermion propagator for excitations near the Fermi surface and the breakdown of the Fermi liquid description. We implement a resummation of these infrared divergences via the Euclidean renormalization group to obtain the spectral density, dispersion relation, widths, and wave function renormalization for single quasiparticles near the Fermi surface. We find that all features scale with anomalous dimensions: ${\omega }_p\mathrm{}\left(k\right)\mathrm{}\propto |k-k_F{|}^{1/\left(1-2\lambda \right)},$ $\Gamma \mathrm{}\left(k\right)\mathrm{}\propto |k-k_F{|}^{1/\left(1-2\lambda \right)};$ $Z_p\mathrm{}\left(k\right)\mathrm{}\propto |k-k_F{|}^{2\lambda /\left(1\mathrm{}-2\lambda \right)}$ with $\lambda =\alpha /6\mathrm{}\pi$ for QED, $({\alpha }_s/6\mathrm{}\pi {\left)\right(N}_c^2-{1)/2N}_c$ for QCD with $N_c$ colors and $N_F$ flavors. The discontinuity of the quasiparticle distribution at the Fermi surface vanishes. For $k\approx k_F$ we find $n_{k\approx k_F}=\sin \left[\pi \lambda \right]/2\mathrm{}\pi \lambda -\left(k-k_F\right)/\pi M\left(1\mathrm{}-4\lambda \right)+\mathcal{O}(k-k_F{)}^2$ with $M$ the dynamical screening scale of magnetic gluons (photons). The dynamical renormalization group is implemented to study nonequilibrium relaxation. The amplitude of single quasiparticle states with momentum near the Fermi surface falls off as $|{\Psi }_{k\approx k_F}\mathrm{}\left(t\right)\mathrm{}|\approx |{\Psi }_{k\approx k_F}{(t}_0\left)|e^{-\Gamma \mathrm{}\left(k\right)\left(t-t_0\right)}\right[t_0/t{]}^{2\lambda }.$ Thus quasiparticle states with Fermi momentum have zero group velocity and relax with a power law with a coupling-dependent anomalous dimension.