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The expressions of the shear viscosity and the bulk viscosity components inthe presence of an arbitrary external magnetic field for a system of hotcharged scalar Bosons (spin-0) as well as for a system of hot charged DiracFermions (spin-$\frac{1}{2}$) have been derived by employing the one-loop KuboFormalism. This is done by explicitly evaluating the thermo-magnetic spectralfunctions of the energy momentum tensors using the real time formalism offinite temperature field theory and the Schwinger proper time formalism. In thepresent work, a rich quantum field theoretical structure in the expressions ofthe viscous coefficients in non-zero magnetic field are found, which aredifferent from their respective expressions obtained earlier via kinetic theorybased calculations; though, in absence of magnetic field, the one-loop Kubo andthe kinetic theory based expressions for the viscosities are known to beidentical. We have identified that Kubo and kinetic theory based results ofviscosity components follow similar kind of temperature and magnetic fielddependency. The relaxation time and the synchrotron frequency in the kinetictheory formalism are realized to be connected respectively with the thermalwidth of propagator and the transitions among the Landau levels of the chargedparticles in the Kubo formalism. We believe that, the connection of latterquantities are quite new and probably the present work is the first timeaddressing this interpretation along with the new expressions of viscositycomponents, not seen in existing works.

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