I'm reading the path integral chapter of Schwartz's "Quantum Field theory and the Standard model". Something seems wrong!(adsbygoogle = window.adsbygoogle || []).push({});

He starts by putting complete sets of states(field eigenstates) in between the vacuum to vacuum amplitude:

## \displaystyle \langle 0;t_f|0;t_i \rangle=\int D\Phi_1(x)\dots D\Phi_n(x) \langle 0|e^{-i\delta t\hat H (t_n)}|\Phi_n\rangle \langle \Phi_n| \dots |\Phi_1\rangle \langle \Phi_1|e^{-i\delta t\hat H (t_0)}|0\rangle \ \ \ \ \ \ (*) ##

Then he computes ## \langle \Phi_{j+1}|e^{-i\delta t\hat H(t_j)}|\Phi_j\rangle ## and says that all these pieces multiply to give:

## \displaystyle \langle 0;t_f|0;t_i\rangle\propto \int D \Phi(\vec x,t) e^{iS[\Phi]}##

My problem is, not all of the factors in (*) are of the form## \langle \Phi_{j+1}|e^{-i\delta t\hat H(t_j)}|\Phi_j\rangle ##. We also have ## \langle 0|e^{-i\delta t\hat H (t_n)}|\Phi_n\rangle ## and ## \langle \Phi_1|e^{-i\delta t\hat H (t_0)}|0\rangle ##. But it seems Schwartz just ignores these two factors!

What's going on here?

Thanks

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# A Path integral formula for vacuum to vacuum amplitude

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