# A Commutator of field operator with arbitrary functions

1. Aug 17, 2016

### eudo

In QFT, the commutation relation for the field operator $\hat{\phi}$ and conjugate momentum is
$$[\phi(x,t),\pi(y,t)] = i\delta(x-y)$$
Maybe this is obvious, but what would the commutator of $\phi$ or $\pi$ and, say, $e^{i k\cdot x}$ be?

2. Aug 17, 2016

### vanhees71

It's obviously 0, because $\exp(\mathrm{i} k \cdot x)$ is just a number, which commutes with all operators.

3. Aug 17, 2016

### eudo

Of course... Thanks