Hello! I read that in Heisenberg picture the propagator from x to y is given by ##<0|\phi(x)\phi(y)|0>##, where ##\phi## is the Klein-Gordon field. I am not sure I understand why. I tried to prove it like this:(adsbygoogle = window.adsbygoogle || []).push({});

##|x>=\phi(x,0)|0>## and after applying the time evolution operator we have ##U(t)|x>=e^{-iHt}\phi(x,0)|0>##. And the propagator should show the overlapping between ##|x>## and ##|y>## at time t. This would be

##<y|U(t)|x>=<0|\phi(y,0)e^{-iHt}\phi(x,0)|0> = <0|e^{-iHt}\phi(y,0)\phi(x,0)|0>## which is not what I was supposed to obtain. I am also not sure about the time dependence of ##\phi## in the propagator. Can someone explain this to me?

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# I Propagator operator in Heinsenberg picture

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