One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized Bosonic and Fermionic systems

Understand

The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar Bosons (spin-0) as well as for a system of hot charged Dirac Fermions (spin-$\frac{1}{2}$) have been derived by employing the one-loop Kubo Formalism.

• This is done by explicitly evaluating the thermo-magnetic spectral functions of the energy momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism.
• In the present work, a rich quantum field theoretical structure in the expressions of the viscous coefficients in non-zero magnetic field are found, which are different from their respective expressions obtained earlier via kinetic theory based calculations; though, in absence of magnetic field, the one-loop Kubo and the kinetic theory based expressions for the viscosities are known to be identical.
• We have identified that Kubo and kinetic theory based results of viscosity components follow similar kind of temperature and magnetic field dependency.