Somehow I have problems with figuring out the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

I know that the scalar field is obeying the follwoing equations:

[tex]<0|\phi(x)|k> = e^{ikx}[/tex]

[tex]<0|\phi(x)^\dag|k> = 0[/tex]

[tex]<k'|\phi(x)^\dag|0> = e^{-ik'x}[/tex]

[tex]<k'|\phi(x)|0> = 0[/tex]

And I was told that I can deduce the following result from the equations above:

[tex]<k'|(\partial_\mu \phi^\dag)\phi|k> = - i k'_\mu e^{-i(k'-k)x}[/tex]

I can 'derive' this when I sandwich a vacuum projector in the lhs:

[tex]<k'|(\partial_\mu \phi^\dag)\phi|k> = (\partial_\mu <k'|\phi^\dag|0>)<0|\phi|k>[/tex]

But I do not understand why I am allowed to do this?

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# Simple QFT question

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