In QFT a scalar field can be expressed as
$$\phi(x)=\int \dfrac{d^3k }{(2\pi)^3\sqrt{2\omega_k}}(a_k(t)+a_{-k}^\dagger(t))e^{i\mathbf{k}\cdot \mathbf{x}}$$
$$\pi(x)=\int \dfrac{d^3k}{(2\pi)^3 \sqrt{2\omega_k}}\left(-i\sqrt{\dfrac{\omega_k}{2}}\right)(a_k(t)-a_{-k}^\dagger(t))e^{i\mathbf{k}\cdot...
Despite being literally a "what am I doing wrong" question (which we generally take to be off topic), I rather like the way the question is asked, and I would kind of like to see it be on topic.
In QFT I've seem a free field being defined as
$$\phi(x)=\int \dfrac{d^3k}{(2\pi)^3\sqrt{2\omega_k}}(a_p e^{-ip_\mu x^\mu}+a_p^\dagger e^{ip_\mu x^\mu})$$
where $a_p$ is time independent and the time dependence is contained in the exponential.
On the other hand, this can be written as
$$\phi(...
Hm, well no harm done since there were no votes, comments, or answers on the earlier question - but we might want to mention to them that deleting and reposting is not preferred
@heather @Kenshin (Einstein?) Physics Problems Q and A website is currently not reachable. Fatal Error message coming up in browser since about 9 hours ago.
In QFT a scalar field can be expressed as
$$\phi(x)=\int \dfrac{d^3k }{(2\pi)^3\sqrt{2\omega_k}}(a_k(t)+a_{-k}^\dagger(t))e^{i\mathbf{k}\cdot \mathbf{x}}$$
$$\pi(x)=\int \dfrac{d^3k}{(2\pi)^3 \sqrt{2\omega_k}}\left(-i\sqrt{\dfrac{\omega_k}{2}}\right)(a_k(t)-a_{-k}^\dagger(t))e^{i\mathbf{k}\cdot...
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