Non-Fermi-liquid aspects of cold and dense QED and QCD: Equilibrium and nonequilibrium - art. no. 034016

We study equilibrium and nonequilibrium aspects of the normal state of cold and dense QCD and QED. The exchange of dynamically screened magnetic gluon s (photons) leads to infrared singularities in the fermion propagator for e xcitations near the Fermi surface and the breakdown of the Fermi liquid des cription, 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 quasiparticl es near the Fermi surface. We find that all features scale with anomalous d imensions: omega (p)(k)proportional to \k-k(F)\(1/(1-2 lambda)), Gamma (k) proportional to \k-k(F)\(1(1-2 lambda)); Z(p)(k)proportional to \k-k(F)\(2 lambda/(1-2 lambda)) with lambda = alpha /6 pi for QED, (alpha (s)/6 pi)(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 imate tok(F) we find n(k)approximate to (kF)=sin[pi lambda]/2 pi lambda-(k- k(F))/piM(1-4 lambda)+O(k-k(F))(2) with M the dynamical screening scale of magnetic gluons (photons). The dynamical renormalization group is implement ed to study nonequilibrium relaxation. The amplitude of single quasiparticl e states with momentum near the Fermi surface falls off as \psi (k approxim ate to kF)(t)\approximate to\psi (k approximate to kF)\(t(0))\e(-Gamma (k)( t-t0))[t(0)/t](2 lambda). Thus quasiparticle states with Fermi momentum hav e zero group velocity and relax with a power law with a coupling-dependent anomalous dimension.