My Quantum Field Theory lecturer just said that $\hat{a}(p)|0\rangle=0$ because the vacuum state contains no particles. Now, according to Wikipedia,
"according to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence".
So is this argument incorrect?
In field theory, there are two vacua. The non-perturbative vacuum $|\Omega\rangle$ and the vacuum of the free theory $|0\rangle$. The wikipedia article makes reference to $|\Omega\rangle$ in terms of $|0\rangle$ and its excitations.
The true vacuum is annihilated by the (dressed) annihilation operators, and can be thought of perturbatively in terms $|0\rangle$ plus fluctuations. Thus $|\Omega\rangle$ is not "empty" if we define as empty $|0\rangle$. But one should keep in mind that this is an artifact of the perturbation theory.
