Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex Klein-Gordon field. Although the procedure is the one followed for the computation of the propagator of the real K-G field, a problem comes up:(adsbygoogle = window.adsbygoogle || []).push({});

As known: <0|T[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> = [itex]\Theta(x^{0}-y^{0})[/itex]<0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> + [itex]\Theta(y^{0}-x^{0})[/itex]<0|[itex]\varphi(y)\varphi^{+}(x)[/itex]|0>

and <0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0>=<0|[itex]\varphi(y)\varphi^{+}(x)[/itex]|0>

But if we try to verify that one of the above correlation functions is a green's function of the K-G equation we hit the obstacle: [itex]\partial_{x}[/itex]<0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> . And I refer to it as an obstacle because of the commutation relation [[itex]\varphi(x),\pi^{+}(y)[/itex]]=0..How could i deal with this calculation..? Thanks in advance.

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# Complex scalar field propagator evaluation.

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