Abstract
An improvement with the correct transformation properties on the previously derived coarse-grained position operator is made. This most general form of the operator may be more useful for physical problems than the previous one. In fact, in addition to the discussions with respect to the microscopic and macroscopic limits, quantum coherence and decoherence in the macroscopic system can be discussed with this general form. It is pointed out that decoherence generally occurs in almost all the macroscopic systems and the realization of the macroscopic coherence is the extremely exceptional case.
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