  A real-time thermal field theoretical calculation of shear viscosity has been
described in the Kubo formalism for bosonic and fermionic medium. The two point
function of viscous stress tensor in the lowest order provides one-loop
skeleton diagram of boson or fermion field for bosonic or fermionic matter.
According to the traditional diagrammatic technique of transport coefficients,
the finite thermal width of boson or fermion is introduced in their internal
lines during the evaluation of boson-boson or fermion-fermion loop diagram.
These thermal widths of $\phi$ boson and $\psi$ fermion are respectively
obtained from the imaginary part of self-energy for $\phi\Phi$ and $\psi\Phi$
loops, where interactions of higher mass $\Phi$ boson with $\phi$ and $\psi$
are governed by the simple $\phi\phi\Phi$ and ${\ov\psi}\psi\Phi$ interaction
Lagrangian densities. A two-loop diagram, having same power of coupling
constant as in the one-loop diagram, is deduced and its contribution appears
much lower than the one-loop values of shear viscosity. Therefore the one-loop
results of Kubo-type shear viscosity may be considered as leading order results
for this simple $\phi\phi\Phi$ and ${\ov\psi}\psi\Phi$ interactions. This
approximation is valid for any values of coupling constant and at the
temperatures greater than the mass of constituent particles of the medium.
