Density matrix of a quantum field in a particle-creating background

Abstract

We consider the time evolution of a quantized field in backgrounds that violate the vacuum stability (particle-creating backgrounds). Our aim is to study the exact form of the final quantum state (the density operator at a final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of the evolution. We find a generating functional that allows us to have the density operators for any initial state. Averaging over states of a subsystem of antiparticles (particles), we obtain explicit forms for reduced density operators for subsystems of particles (antiparticles). Studying one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g. gluons) in an initial state increases the creation rate of the same kind of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not a thermal equilibrium. In this respect, we discuss some cases when a pair creation by an electric-like field can mimic a one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we study the time and temperature behavior of mean numbers of created particles provided switching on and off effects of the external field are negligible. It is shown that at high temperatures and in slowly varying electric fields the rate of particle creation is essentially time-dependent.