In Zee's book at page 12 in both editions he finds that he can write the amplitude(adsbygoogle = window.adsbygoogle || []).push({});

$$\langle q_f|e^{-iHT} |q_i\rangle = \int Dq(t) e^{iS} $$

where T is the time between emission at ##q_i## and observation at ##q_f##. He then states that we often define

$$Z = \langle 0 | e^{-iHT} |0 \rangle $$

And he observes that by inserting a complete set of states we can write

$$ Z = \int q_f \int q_i \langle 0 | q_f\rangle \langle q_f | e^{-iHT} |q_i\rangle \langle q_i |0 \rangle = int q_f \int q_i \psi_0^* (q_f) \psi_0 (q_i) \langle q_f | e^{-iHT} |q_i\rangle. $$

But then a few sentences down he writes

$$Z = \int Dq(t) e^{iS}. $$

Is there an error in Zee here or ##Z## as defined above actually equal to the path integral given by ##\langle q_f|e^{-iHT} |q_i\rangle##? If so, how does the integration over the ground state wavefunction vanish?

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# Interpretation of the functional Z (in Zee).

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