Dielectric functions and dispersion relations of ultra-relativistic plasmas with collisions

In the present paper, we calculate the dielectric functions of an ultra-relativistic plasma, such as an electron–positron or a quark–gluon plasma. We use classical transport theory and take into account collisions within the relaxation time approximation. From these dielectric functions we derive the dispersion relations of longitudinal and transverse plasma waves. PACS Nos.: 12.38.Mh, 52.25.Dg, 52.27.Ep, 52.35.Hr