Semiclassical approximation meets Keldysh–Schwinger diagrammatic technique: scalar $$\varphi ^4$$

We study the evolution of non-equilibrium quantum fields from a highly excited initial state in two approaches: standard Keldysh-Schwinger diagram technique and semiclassical expansion. demonstrate explicitly that these approaches coincide if coupling constant $g$ Plank $\hbar$ are small simultaneously. Also, we discuss loop diagrams perturbative approach, which summed up by leading order term As an example, consider shear viscosity for scalar field theory at order. introduce new unifies both diagrammatic open possibility to perform resummation contributions.