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Questions about Peskin QFT

  1. Jul 10, 2008 #1
    Dear all,

    While I was reading chap2 of Peskin, I got some questions.
    (1) The vanishment of the commutator of fields [tex][\phi(x),\phi(y)]=0[/tex] means that the measurements at [tex]x[/tex] and [tex]y[/tex] do not interfere at all. Is this a postulate? Is this the so-called micro-causality?

    (2) How Peskin deform the contour of fig.2.3 ? Why the two contour integrals are the same?

    (3) How to prove if [tex]x,y[/tex] are space-like separated, there is a continuous Lorentz transformation take [tex]x-y[/tex] to [tex]-(x-y)[/tex]? i.e. I don't understand fig.2.4.

    Thanks for anyone.
  2. jcsd
  3. Jul 12, 2008 #2


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    Yes, this is the microcausality condition.

    If they are spacelike separated you can define a spacelike vector V that connects them. Then, you can easily show that there exists a Lorentz transformation that transforms V into -V. This will be a rotation of 180 degrees. If you try the same procedure for two points within the light-cone, connected by a timelike vector, you will see that the transformation is not possible.
  4. Jul 12, 2008 #3
    Thanks. I guessed this is a "postulate", however, the book didn't give a clear assertion that this is a postulate. So I doubt that this can be derived. Now I think it is a postulate of QFT.
    Thanks, I got it. But it seems that the argument have to be slightly modified. If V is a spacelike vector, we need not only the rotation to transform V into -V. Because the temporal coordinate is flipped too, so I guess we need a boost also.

    Thanks for the discussion!
  5. Jul 13, 2008 #4


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    I started a thread a time ago with a similar question. You may want to use the search function to find it. It seems it is actually a postulate: it can be derived for specific representations such as the Fock representation that, however, restricts itself to positive mass solutions. There is no general way to derive it.

    Yes, but I think that a boost will not do the work to completely transform V into -V if it is timelike.
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