The main focus of this article is to obtain various transport coefficients for a hot QCD medium that is produced while colliding two heavy nuclei ultra-relativistically. As the hot QCD medium follows dissipative hydrodynamics while undergoing space-time evolution, the knowledge of the transport coefficients such as thermal conductivity, electrical conductivity, shear and bulk viscosities are essential to understand the underlying physics there. The approach adopted here is semi-classical transport theory. The determination of all these transport coefficients requires knowledge of the medium away from equilibrium. In this context, we setup the linearized transport equation employing the Chapman-Enskog technique from kinetic theory of many particle system with a collision term that includes the binary collisions of quarks/antiquarks and gluons. In order to include the effects of a strongly interacting, thermal medium, a quasi-particle description of realistic hot QCD equation of state has been employed through the equilibrium modeling of the momentum distributions of gluons and quarks with non-trivial dispersion relations while extending the model for finite but small quark chemical potential. The effective coupling for strong interaction has been redefined following the charge renormalization under the scheme of the quasiparticle model. The consolidated effects on transport coefficients are seen to have significant impact on their temperature dependence. The relative significances of momentum and heat transfer as well as charge diffusion processes in hot QCD have been investigated by studying the ratios of the respective transport coefficients.

We evaluate the shear viscosity of a pion gas in the relativistic kinetic theory approach. The in-medium propagator of the ρ meson at finite temperature is used to evaluate the π − π scattering amplitude in the medium. The real and imaginary parts of the self-energy calculated from one-loop diagrams are seen to have noticeable effects on the scattering cross-section. The consequences on temperature dependence of the shear viscosity evaluated in the Chapman-Enskog and relaxation time approximations are studied.

The bulk and shear viscosities of a pion gas is obtained by solving the relativistic transport equation in the Chapman-Enskog approximation. In-medium effects are introduced in the $\pi\pi$ cross-section through one-loop self-energies in the propagator of the exchanged $\rho$ and $\sigma$ mesons. The effect of early chemical freeze-out in heavy ion collisions is implemented through a temperature dependent pion chemical potential. These are found to affect the temperature dependence of the bulk and shear viscosities significantly

In this article, shear viscosity, bulk viscosity, and thermal conductivity of a hot QCD medium have been studied in the presence of strong magnetic field. To model the hot magnetized QCD matter, an extended quasi-particle description of the hot QCD equation of state in the presence of the magnetic field has been adopted. The effects of higher Landau levels on the temperature dependence of viscous coefficients (bulk and shear viscosities) and thermal conductivity have been obtained by considering the 1 → 2 processes in the presence of the strong magnetic field. An effective covariant kinetic theory has been set up in (1+1)-dimensional that includes mean field contributions in terms of quasi-particle dispersions and magnetic field to describe the Landau level dynamics of quarks. The sensitivity of these parameters to the magnitude of the magnetic field has also been explored. Both the magnetic field and mean field contributions have seen to play a significant role in obtaining the temperature behaviour of the transport coefficients of hot QCD medium.