Nonperturbative calculation of the shear viscosity in hot φ4 theory in real time

Starting from the Kubo formula we calculate the shear viscosity in hot φ4 theory nonperturbatively by resumming ladders with a real-time version of the Bethe-Salpeter equation at finite temperature. In the weak coupling limit, the generalized Fluctuation-Dissipation Theorem is shown to decouple the Bethe-Salpeter equations for the different real-time components of the 4-point function. The resulting scalar integral equation is identical with the one obtained by Jeon using diagrammatic “cutting rules” in the Imaginary Time Formalism.