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Generating Functional in Momentum Space -- QFT

  1. Apr 28, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi,

    Question attached:

    questionbabayy.png

    inserting ##\phi (x)= \int \frac{d^4k}{(2\pi)^2}\phi(x)e^{-i k_u x^u}##
    and similar for ##J(x) ## / ##J(k)## into the action and then integrating over ##k## gives:

    Solution attached:

    solutionbabay.png

    I AM STUCK on this part, completing the square ; so I see we get back the term ##\frac{-h}{i}J(k)\phi(-k)## however don't we also get an additional identiical term ##J(-k)\phi (k)##?


    What has happened to this?!

    Many thanks in advance.

    2. Relevant equations

    see above
    3. The attempt at a solution
    see above
     
  2. jcsd
  3. May 3, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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