The Chapman-Enskog expansion is applied to the relativistic transport equation to find the transport coefficients of pure quark and gluon matter, as well as those of a quark-antiquark mixture and a zero baryon number quark-antiquark-gluon plasma. The results for the simple quark and gluon system are larger but still comparable with values obtained from similar calculations in the literature. the scattering integrals are divergent due to the exchange of transverse gluons. However, by introducing suitable cutoffs and Coulomb-like logarithms, these integrals can be regularized.
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