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Mensky has suggested to account for "continuous measurement" by attaching toa path integral a weight function centered around the classical path that theintegral assigns a probability amplitude to. We show that in fact this weightfunction doesn't have to be viewed as an additional ingredient put in by hand.It can be derived instead from the conventional path integral if theinfinitesimal term i\epsilon\ in the propagator is made finite; the "classicaltrajectory" is proportional to the current.

Link between quantum measurement and the i\epsilon\ term in the QFT propagator