Hello, I'm having trouble calculating this commutator, at the moment I've got:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\left[a_{p},a_{q}^{\dagger}\right]=\left[\frac{i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p),\frac{-i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p)\right]=i\left[\Pi(p),\Phi(q)\right]=i\int d^{3}x d^{3}ye^{-i(\vec{p}\bullet\vec{x}+\vec{q}\bullet\vec{y})}\left[\Pi(x),\Phi(y)\right]=\int d^{3}x d^{3}ye^{-i(\vec{p}\bullet\vec{x}+\vec{q}\bullet\vec{y})}\delta^{3}(x-y)=\int d^{3}x e^{-i(\vec{p}+\vec{q})\bullet\vec{x}}=(2\pi)^{3}\delta^{3}(p+q)[/itex]

But I should get [itex](2\pi)^{3}\delta^{3}(p-q)[/itex] instead. Where have I made the mistake?

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# Commutation relation of the creation/annihilation operators in a field

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