Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar $\varphi^4$

Understand

We study the evolution of the non-equilibrium quantum fields from a highly excited initial state in two approaches: the standard Keldysh-Schwinger diagram technique and the semiclassical expansion.

• We demonstrate explicitly that these two approaches coincide if the coupling constant $g$ and the Plank constant $\hbar$ are small simultaneously.
• Also, we discuss loop diagrams of the perturbative approach, which are summed up by the leading order term of the semiclassical expansion.
• As an example, we consider shear viscosity for the scalar field theory at the leading semiclassical order.