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A quantitative quantum field approach with non-local order parameters ispresented for a very weakly interacting, dilute Bose gas. Within the presentedmodel, which assumes the constraint of particle number conservation at constantaverage energy in the canonical ensemble, it is shown that both coherentoscillations, as well as decay times of quantum coherence for the forward andbackward propagating components of the quantum field created by the atomiccloud of a very weakly interacting Bose-Einstein condensate, are defined by aunique time variable. Within the present numerical theory, a quantitativeestimate for the unit time scale for time propagation of a particle in a veryweakly interacting Bose gas is derived from the coherence time of the wavefield and it is illustrated that this time scale defines a unit time fortransitions between different realizations of the Boltzmann equilibrium asdefined by the maximum entropy from the vanishing of the chemical potential.

Finite phase coherence time of a bosonic quantum field at the Boltzmann equilibrium