  A quantitative quantum field approach with non-local order parameters is
presented for a very weakly interacting, dilute Bose gas. Within the presented
model, which assumes the constraint of particle number conservation at constant
average energy in the canonical ensemble, it is shown that both coherent
oscillations, as well as decay times of quantum coherence for the forward and
backward propagating components of the quantum field created by the atomic
cloud of a very weakly interacting Bose-Einstein condensate, are defined by a
unique time variable. Within the present numerical theory, a quantitative
estimate for the unit time scale for time propagation of a particle in a very
weakly interacting Bose gas is derived from the coherence time of the wave
field and it is illustrated that this time scale defines a unit time for
transitions between different realizations of the Boltzmann equilibrium as
defined by the maximum entropy from the vanishing of the chemical potential.
