The shear viscosity of quark-gluon plasma under anisotropic scatterings

Quark-gluon plasma (QGP) is a state of matter that is formed from relativistic heavy-ion collisions and also in the early universe. The quarks and gluons as quasi-free particles resemble an expanding viscous liquid under extremely high temperatures and densities. The shear viscosity, ??, of the QGP under isotropic scatterings in full equilibrium (meaning thermal and chemical equilibrium) is already known analytically and numerically. Analytically, the viscosity obtained via the Chapman-Enskog (CE) method agrees well with the numerical Green-Kubo values for the viscosity under anisotropic scatterings as well as isotropic scatterings. In this thesis, we use the CE formula, along with other approximation methods, for viscosity to derive ??/?? and compare the analytical curves with the numerical values for forward-angle scatterings. My contribution is the correction of two typos in the published CE and ModRTA formulae of viscosity and the application of all obtained formulae to three-dimensional expansion cases under full and partial equilibrium. This includes the calculations of shear viscosity, entropy density, and the ??/?? ratio of the parton system from the AMPT model as a function of time of the parton evolution