LANDAU GHOSTS AND ANTI-GHOSTS IN CONDENSED MATTER AND HIGH DENSITY HADRONIC MATTER
It is observed that the "ghost" (originally discovered by Landau in quantum electro-dynamics) and its counterparts in other theories are indeed ubiquitous as they occur in a one-loop approximation to any conventional (unbroken) gauge theory. The mechanism is first exposed in its generality via the Dyson equation and a simple but explicit example in condensed matter is provided through the static Clausius–Mossotti equation and its dynamic counterpart, the Lorenz–Lorentz equation. The physical phase transition phenomenon associated with it is found to be super-radiance. We verify quantitatively that water (and many other polar liquids) are indeed super-radiant at room temperature. In quantum chromo-dynamics on the other hand, we encounter, thanks to asymptotic freedom, an "anti-ghost" which is closely associated with color confinement. Thus, in QCD, free quarks and glue exist in a super-radiant phase and hadronic matter exists in the normal one.