In Peskin and Schroeder, we calculate that the propagator [itex]D(x-y)=\langle 0|\phi(x)\phi(y)|0\rangle[/itex] to be non zero even if x and y are space-like separated (although it's exponentially decaying). This suggests (given our interpretation of this quantity) that a particle CAN propagate between these two points (albeit with vanishingly small probability).(adsbygoogle = window.adsbygoogle || []).push({});

Peskin argues, however, that this is not a violation of causality, because causality should only prevent measurements from affecting each other over space-like separations. He goes on to say that, we really should calculate:

[tex]\langle 0|[\phi(x),\phi(y)]|0\rangle[/tex]

And that since this is 0, causality is preserved. Can someone elaborate this point for me? I'm not sure I quite understand what the commutator has to do with measurements, and why it is this quantity that is important and not the D(x-y) which is important.

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# Preserving Causality in QFT

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