Commutator of field operator with arbitrary functions

[eudo]

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

 

[vanhees71]

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

 

[eudo]

Of course... Thanks