0
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(...