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I read chapter 7.1 of "An Introduction to Quantum Field Theory" by Peskin and Schröder and have two questions.

They derive the two point function for the interacting case.

On page 213 they manipulate the matrix element, after insertion of the complete set of eigenstates.

[tex] <\Omega | \Phi (x) | \lambda_p > [/tex]

[tex] = < \Omega | e^{iPx} \Phi (0) e^{- iPx} | \lambda_p > [/tex]

[tex] = < \Omega | \Phi (0) | \lambda_p > e^{- ipx} \end{array} [/tex]

with [tex] E_p = p^0[/tex]

1. Could anyone explain to me, how they get the third line above (also see P & S: equation (7.4) ) ?

2. Later on page 215 they make a Fourier Transform of the spectral decomposition. I don't know, how they derive equation 7.9

[tex] \int d^4 x e^{ipx} < \Omega | T \Phi (x) \Phi(0) | \Omega> = \frac{iZ}{p^2 - m^2 + i \epsilon} + \int_{~4m^2}^{\infty} \frac{d M^2}{2 \pi} \rho(M^2) \frac{i}{p^2 - M^2 + i \epsilon} [/tex]

Regards,

Mr. Fogg

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# Peskin Schröder Chapter 7.1 Field Strength Renormalization

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