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Decoherence as Projection

This article has left me confused. I don't see how this notion of phase relates back to a locally-evolving amplitude distribution over a space of configurations, if those configurations are merely the locations of some indistinguishable lumps in a field. How do these phases become manifest in the configuration space? It seems like there must be more to the configuration space than just a set of locations for each type of "particle", but previous articles have claimed otherwise.