#normal order

PHY2403: QFT I: Momentum of scalar field: time dependent terms?

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Way back in lecture 8, it was claimed that \begin{equation}\label{eqn:momentum:20} P^k = \int d^3 x \hat{\pi} \partial^k \hat{\phi} = \int \frac{d^3 p}{(2\pi)^3} p^k a_\Bp^\dagger a_\Bp. \end{equation} If I compute this, I get a normal ordered variation of this operator, but also get some time dependent terms. Here’s the computation…