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I'm currently self studying QFT from Matthew D. S textbook and David Tongs online notes. I have trouble understanding the creation/annihilation operators in the QFT formalism. I couldn't find any equation of the $a_p$ and $a_q$, where $p$ and $q$ are momentum 3-vectors. What is there meaning (physically or analogically?). Is there any equation of $a_p$ = and $a_q$ ?

Qmechanic
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  • Do you recall the formalism of these operators from quantum mechanics and the harmonic oscillator? – Triatticus Jul 18 '18 at 12:01
  • I understand the operators in the Schrodinger formalism where they are used as ladder operators switching to the upper or lower quantum state. What's the difference in these operators? Also, does q and p represent space and conjugate momentum in the indices? or is it just a simple for a different vector? –  Jul 18 '18 at 12:43
  • Related, possibly slightly, sorry....https://physics.stackexchange.com/questions/415433/annihilation-and-creation-operators-in-qft. But this is better, I think https://physics.stackexchange.com/questions/412568/creation-and-annihilation-operators-in-qft –  Jul 18 '18 at 13:50
  • Hint: use the relation between $\phi$ and $\pi$ on one hand and $a_p$ and $a_p^{\dagger}$ on another. Invert the relation to get the expressions for $a_p$ and $a_p^{\dagger}$. – Prof. Legolasov Jul 18 '18 at 15:01

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