Quantum corrections to the classical statistical approximation for the expanding quantum field

Abstract

Abstract We calculate quantum corrections to the classical statistical approximation (CSA) within the Keldysh–Schwinger technique for both static and longitudinally expanding scalar fields. Relaxation of highly excited quantum fields is naturally described in terms of semiclassical approaches, such as CSA. However, the expansion of the system reduces the applicability of semiclassical approaches making quantum corrections important. We study nonequilibrium evolution of the trace of the energy–momentum tensor of the homogeneous static and the longitudinally expanding scalar field. It turns out that, for an expanding field, the calculated equation of state can differ from ultrarelativistic one due to the quantum corrections. We provide analytical and numerical arguments for the appearance of the nontrivial intermediate regime of the evolution of the expanding matter where quantum corrections are significant.