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    $\begingroup$ Hint: $\int d^3 x \, e^{i \vec{k} \cdot \vec{x}} =(2 \pi)^3 \delta^{(3)}(\vec{k})$. $\endgroup$
    – Hyperon
    Commented Dec 19, 2022 at 16:01
  • $\begingroup$ this I figured I would have to use, my problem is with causing terms such as $a_p^{s\dagger}b_q^r$ to vanish. $\endgroup$
    – Nitzan R
    Commented Dec 19, 2022 at 16:06
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    $\begingroup$ Second hint: You have $\psi^\dagger$ in your expression for the momentum operator (which is correct) but you seem to insert $\bar{\psi}$ in your further calculation. $\endgroup$
    – Hyperon
    Commented Dec 19, 2022 at 16:17
  • $\begingroup$ Last hint: $v_s^\dagger(-\vec{p}) u_r(\vec{p})=?$ Eq. (3.65) on p. 48 of Peskin/Schroeder might be helpful. $\endgroup$
    – Hyperon
    Commented Dec 19, 2022 at 17:27