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Homework Statement
Problem with the ordering of integrals in the derivation of the Lehmann-Kaller form of the exact propagator in Srednicki's book.
We start with the definition of the exact propagator in terms of the 2-point correlation function and introduce the complete set of momentum eigenstates and then define a certain spectral density in terms of a delta function. But the spectral density is also a function of 'k', so we cannot take the spectral density outside the integral over 'k'. Since that is not possible, the subsequent manipulations fail too.
Homework Equations
In Srednicki's book :
Equation 13.11 and 13.12
If that is incorrect, the use of 13.15 to get 13.16 is not possible.
The Attempt at a Solution
I don't see how it is possibe to derive the equation without that interchange.
I'd appreciate any clarifications on this issue. Am I missing some trivial thing?