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Total momentum operator for free scalar field

  1. Aug 23, 2013 #1
    Sorry for reopening a closed thread. But I have exactly the same doubt as this guy: https://www.physicsforums.com/showthread.php?t=346730
    And the answer doesn't actually answer his question. I do get delta(p+p'), but they just help me in getting [itex]a_{p}a_{-p}[/itex] and [itex]a_{p}^{\dagger}a_{-p}^{\dagger}[/itex] Which I don't know how to get rid off, and shouldn't be in the final answer.
  2. jcsd
  3. Aug 23, 2013 #2


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    You have at last to integrate over d3p. Your unwanted term is p ap a-p, and from the diametrically opposite value of p you'll get -p a-p ap. But the operators commute, so this is equivalently -p ap a-p, which cancels with the first term.
  4. Aug 23, 2013 #3
    Oh true, that's it! Thank you very much!
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