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So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model" and in the second requirement, he wanted me to show that the action of the conjugate momentum operator $\hat{\pi}$ on $\hat{\phi}$ eigenstate is equal to the the action of the variation of $\phi$ to the same eigenstate:

$$ \langle\phi|\hat{\pi}(x) = -i\hbar \frac{\delta} { \delta \phi(x)} \langle\phi| $$

and I am stuck in that requirement.

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  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/576974/2451 , physics.stackexchange.com/q/76299/2451 $\endgroup$
    – Qmechanic ♦
    Commented Dec 20, 2023 at 7:54
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    $\begingroup$ I think the question is simply wrong due to a misuse of notation. It should be $\langle \phi|\pi(x)|\Psi\rangle =- i\hbar (\delta/\delta \phi(x))\langle\phi |\Psi\rangle$ by analogy with the quantum mechnics question in the "duplicate". $\endgroup$
    – mike stone
    Commented Dec 20, 2023 at 14:46

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