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A Commutator of field operator with arbitrary functions

  1. Aug 17, 2016 #1
    In QFT, the commutation relation for the field operator [itex]\hat{\phi}[/itex] and conjugate momentum is
    [\phi(x,t),\pi(y,t)] = i\delta(x-y)
    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?
  2. jcsd
  3. Aug 17, 2016 #2


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    It's obviously 0, because ##\exp(\mathrm{i} k \cdot x)## is just a number, which commutes with all operators.
  4. Aug 17, 2016 #3
    Of course... Thanks
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