Viscosity of the Scalar Fields from the Classical Theory

Abstract

We show how the resummation for time dependent quantities at high temperature can be performed with an effective classical theory. As an application we demonstrate that the leading term in the shear viscosity, which is related to the ${\rho }_{{\Phi }^2{\Phi }^2}$ spectral function can be calculated classically, either using classical linear response theory or from the classical ${\Phi }^2$ correlation function. The classical result depends explicitly on the cutoff, and the choice $\Lambda \sim T$ reproduces the known quantum result.

11 pages, LaTeX, 1 eps figure

References in corpus (3)

• Classical approximation for time dependent quantum field theory: diagrammatic analysis for hot scalar fields
• Classical Statistical Mechanics and Landau Damping
• Classical Limit for Scalar Fields at High Temperature

Cited by in corpus (5)

• Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar ${\phi }^4$
• Divergences in Real-Time Classical Field Theories at Non-Zero Temperature
• Effective theory for the soft fluctuation modes in the spontaneously broken phase of the N-component scalar field theory
• Shear viscosity of the ${\Phi }^4$ theory from classical simulation
• Effective Classical Theory for Real-Time SU(N) Gauge Theories at High Temperature