J. Baacke et al., Initial time singularities in nonequilibrium evolution of condensates and their resolution in the linearized approximation - art. no. 045023, PHYS REV D, 6304(4), 2001, pp. 5023
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.