I've got a question about about eqns. 13.12, 13.13, and 13.16. in Mark Srednicki's QFT book, freely previewable here:(adsbygoogle = window.adsbygoogle || []).push({});

http://www.physics.ucsb.edu/~mark/qft.html

(it's a good book - this is the only section I have problems with)

I don't really get how he derives the Lehmann-Kallen form of the exact propagator. The spectral density in equation 13.11 is a function of total momentum k. In eqn 13.12 and 13.13, the spectral density is taken out of the integration over k, which seems illegal. In deriving eqn 13.16 using 13.15, once again it seems that's only legal if the spectral density is independent of k. How is this all legal?

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# Exact propagator

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