Low Energy Dynamics in Ultradegenerate QCD Matter

We study the low energy behavior of QCD Green functions in the limit that the baryon chemical potential is much larger than the QCD scale parameter $\Lambda_QCD$. We show that there is a systematic low energy expansion in powers of $(\omega/m)^{1/3}$, where $\omega$ is the energy and $m$ is the screening scale. This expansion is valid even if the effective quark-gluon coupling $g$ is not small. The expansion is purely perturbative in the magnetic regime $|\vec{k}| \gg k_0$. If the external momenta and energies satisfy $k_0 \sim |\vec{k}|$, planar, abelian ladder diagrams involving the full quark propagator have to be resummed but the corresponding Dyson-Schwinger equations are closed.