Shear viscosity of hot scalar field theory in the real-time formalism

TL;DR

This paper derives a nonperturbative expression for shear viscosity in hot scalar field theory using the real-time formalism, confirming previous results and providing a comprehensive framework for such calculations.

Contribution

It introduces a general nonperturbative formula for shear viscosity in the real-time formalism, utilizing the Bethe-Salpeter equation and fluctuation-dissipation theorem, applicable to various scalar interactions.

Findings

Confirms leading order shear viscosity matches imaginary time results.

Decouples Bethe-Salpeter equation in (r,a) basis for simplification.

Provides a unified real-time approach for shear viscosity calculation.

Abstract

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called (r,a) basis. The general result is applied to scalar field theory with pure lambda*phi**4 and mixed g*phi**3+lambda*phi**4 interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.