There is this thing I got confused:

Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete base. It is usually referred to as a statement about locality---if microcausality is broken then the "local" operators are not that "local".

There is another statement about the notion of "locality" in S-matrix language---an S-matrix have poles corresponding to particle exchange, and the residue factorizes into S-matrices of sub scattering processes in the limit that these processes happen far from each other. It is in the line of cluster decomposition principle.

So my question is: do these two statements somehow have connections to each other, or even are equivalent? Or they are simply two very different statement and not connected at all?


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