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Annihilation operator acting on a Fock state

  1. Dec 28, 2011 #1
    I'm trying to show:

    a(p)|q1,q2,...,qN> =
    [itex]\sum[/itex]Ni=1(2pi)32Ep\delta(3)(p-qi)x|qi,...,qi-1,qi+1,...,qN>

    I'm pretty sure you have to turn the ket into a series of creation operators acting on the vacuum |0>, but then not sure what relations need to be invoked for it to be clear.

    Any help would be appreciated.
     
  2. jcsd
  3. Dec 30, 2011 #2

    strangerep

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    You might get more help if you attempt a little more yourself, according to the PF rules for homework help. For starters, write down the canonical commutation relations between the a/c operators, and the rules for how they act individually on the vacuum. Then try and do the N=2 case.

    It might also help if you mention which textbook you're working from.
     
  4. Dec 30, 2011 #3
    O.K., so you just use the relation:

    a(p)a+(q) = [a(p),a+(q)] + a+(q)a(p)

    for each case.

    Also can I just clarify that in the answer when it says:

    |qi-1> if i=1, is that just ignored?

    I' learning form these notes:

    http://www.hep.man.ac.uk/u/pilaftsi/QFT/qft.pdf

    With the aide of peskin and schroeder.

    Thank you
     
  5. Dec 30, 2011 #4

    strangerep

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    OK, so now try to do the N=1 case explicitly, using equations (2.29), (2.35) and maybe (2.36) from P&S.

    I think it's the vacuum [itex]|0\rangle[/itex].
     
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