Initial time singularities in nonequilibrium evolution of condensates and their resolution in the linearized approximation - art. no. 045023

The real time nonequilibrium evolution of condensates in field theory requi res an initial value problem specifying an initial quantum state or density matrix. Arbitrary specifications of the initial quantum state (pure or mix ed) results in initial rime singularities. These initial time singularities are of a different nature and independent of the ultraviolet divergences w hich are removed by the usual renormalization counterterms. The removal of the initial time singularities requires a specific choice of initial states . We study the initial rime singularities in the linearized equation of mot ion for the scalar condensate in a renormalizable Yukawa theory in 3 + 1 di mensions, In this renormalizable theory the initial time singularities are enhanced. We present a consistent method for removing these initial time si ngularities by specifying initial states where the distribution of high ene rgy quanta is determined by the initial conditions and the interaction effe cts. This is done through a Bogoliubov transformation which is consistently obtained in a perturbative expansion. The usual renormalization counterter ms and the proper choice of the Bogoliubov coefficients lead to a singulari ty free evolution equation. We establish the relationship between the evolu tion equations in the linearized approximation and linear response theory, It is found that only a very specific form of the external source for linea r response leads to a real time evolution Equation which is singularity fre e. We focus on the evolution of spatially inhomogeneous scalar condensates by implementing the initial state preparation via a Bogoliubov transformati on up to one loop, As a concrete application, the evolution equation for an inhomogeneous condensate is solved analytically acid the results are caref ully analyzed. Symmetry breaking by initial quantum states is discussed.