Hard Dense Loops in a Cold Non-Abelian Plasma

Classical transport theory is used to study the response of a non-Abelian plasma at zero temperature and high chemical potential to weak color electromagnetic fields. In this article the parallelism between the transport phenomena occurring in a non-Abelian plasma at high temperature and high density is stressed. Particularly, it is shown that at high densities it is also possible to relate the transport equations to the zero-curvature condition of a Chern-Simons theory in three dimensions, even when quarks are not considered ultrarelativistic. The induced color current in the cold plasma can be expressed as an average over angles, which represent the directions of the velocity vectors of quarks having Fermi energy. From this color current it is possible to compute $n$-point gluonic amplitudes, with arbitrary $n$. It is argued that these amplitudes are the same as the ones computed in the high chemical potential limit of QCD, that are then called hard dense loops. The agreement between the two different formalisms is checked by computing the polarization tensor of QED due to finite density effects in the high density limit.