Quantum corrections to the Classical Statistical Approximation for the expanding quantum field

We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of Classical Statistical Approximation (CSA). However, the expansion of the system reduces the applicability of such a semiclassical approach as the CSA making quantum corrections important. We calculate the evolution of the trace of the energy-momentum tensor within the Keldysh-Schwinger framework for static and longitudinal expanding geometries. We provide analytical and numerical arguments for the appearance of the nontrivial intermediate regime where quantum corrections are significant

Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar φ4\varphi^4

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. We introduce the new technique that unifies both semiclassical and diagrammatic approaches and open the possibility to perform the resummation of the semiclassical contributions.Comment: 10 pages, many diagram

Scaling laws for the elastic scattering amplitude

The partial differential equation for the imaginary part of the elastic scattering amplitude is derived. It is solved in the black disk limit. The asymptotical scaling behavior of the amplitude coinciding with the geometrical scaling is proved. Its extension to preasymptotical region and modifications of scaling laws for the differential cross section are considered.Comment: 6 p. arXiv admin note: substantial text overlap with arXiv:1206.547