The steps essentially involved in the evaluation of transport coefficients in linear response theory using Kubo formulas are to relate the defining retarded correlation function to the corresponding time-ordered one and to evaluate the latter in the conventional perturbation expansion. Here we evaluate the viscosities of a pion gas carrying out both the steps in the real-time formulation. We also obtain the viscous coefficients by solving the relativistic transport equation in the Chapman-Enskog approximation to leading order. An in-medium π π cross-section is used in which spectral modifications are introduced in the propagator of the exchanged ρ.
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