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Peskin and Schroeder derivation of Klein-Gordon propagator

  1. Feb 22, 2014 #1
    In page 30 of book "An introduction to quantum field theory" by Peskin and Schroeder in the derivation of Klein-Gordon propagator, why p^0=-E_p in the second step in equation (2.54). and why change "ip(x-y)" to "-ip(x-y)"? I thought a lot time, but get no idea. Thank you for your giving me an explanation.
     
    Last edited: Feb 22, 2014
  2. jcsd
  3. Feb 22, 2014 #2

    strangerep

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    Science Advisor

    It took me a long time to figure that out too, when I first studied P+S.

    First, look at this 1D integral:
    $$
    \int_{-\infty}^{+\infty} dp \; e^{-ipx} ~.
    $$ If you perform a change of dummy variable ##p \to p' = -p##, what do you get?

    So in the 2nd step of (2.54), they're just converting the ##e^{ip\cdot(x-y)}## of the 2nd term in the last line on the previous page 29, so that both exponentials are the same, i.e., ##e^{-ip\cdot(x-y)}##. (The latter explains "why p^0=-E_p").
     
  4. Feb 22, 2014 #3
    Thank you!!!
     
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