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We present a generic Markovian master equation inducing the gradualclassicalization of a bosonic quantum field. It leads to the decoherence ofquantum superpositions of field configurations, while leaving the Ehrenfestequations for both the field and the mode-variables invariant. We characterizethe classicalization analytically and numerically, and show that thesemiclassical field dynamics is described by a linear Boltzmann equation in thefunctional phase space of field configurations.

Decoherence of nonrelativistic bosonic quantum fields