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While writing this reply on Physics.SE I thought to myself that it is curious that this tight relation between the topics in the title here is rarely made explict in introductions.
Then next occurred to me the observation that, unfortunately, not even the $n$Lab did seem to say this. So therefore I have now briefly copied my reply there also to S-matrix β Formalization and to FQFT β Idea β General.
This deserves to be expanded on much further, of course, but at least itβs a start now.
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