Nonperturbative calculation of the shear viscosity in hot phi**4 theory in real time

TL;DR

This paper presents a nonperturbative real-time calculation of shear viscosity in hot phi^4 theory using ladder resummation and the Bethe-Salpeter equation, confirming previous diagrammatic results.

Contribution

It introduces a real-time approach to compute shear viscosity nonperturbatively, connecting the Bethe-Salpeter equation with the Imaginary Time Formalism results.

Findings

Shear viscosity computed nonperturbatively in hot phi^4 theory.

Decoupling of Bethe-Salpeter equations in weak coupling limit.

Equivalence with Jeon's diagrammatic approach.

Abstract

Starting from the Kubo formula we calculate the shear viscosity in hot phi**4 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.