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A real-time thermal field theoretical calculation of shear viscosity has beendescribed in the Kubo formalism for bosonic and fermionic medium. The two pointfunction of viscous stress tensor in the lowest order provides one-loopskeleton 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 internallines during the evaluation of boson-boson or fermion-fermion loop diagram.These thermal widths of $\phi$ boson and $\psi$ fermion are respectivelyobtained 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 ${\ov\psi}\psi\Phi$ interactionLagrangian densities. A two-loop diagram, having same power of couplingconstant as in the one-loop diagram, is deduced and its contribution appearsmuch lower than the one-loop values of shear viscosity. Therefore the one-loopresults of Kubo-type shear viscosity may be considered as leading order resultsfor this simple $\phi\phi\Phi$ and ${\ov\psi}\psi\Phi$ interactions. Thisapproximation is valid for any values of coupling constant and at thetemperatures greater than the mass of constituent particles of the medium.

A real-time thermal field theoretical analysis of Kubo-type shear viscosity : Numerical understanding with simple examples