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Checking integration over 4-momentum

  1. Oct 3, 2013 #1
    1. The problem statement, all variables and given/known data
    I would like to make sure I am performing the integration correctly. It is a loop integral in QFT:
    [itex]\int \frac{d^{4}p}{(2\pi)^{4}}\frac{1}{p^{2}}[/itex]
    where p is the 4-momentum, Minkowski space.


    2. Relevant equations



    3. The attempt at a solution
    I think you must change to spherical coordinates in which:
    [itex]d^{4}p=|p|^{3}sin^{2}\theta sin\phi_{1}d|p|d\theta d\phi_{1}d\phi[/itex]
    where [itex]|p|=\sqrt{p_{1}^{2}+p_{2}^{2}+p_{3}^{2}-p_{0}^{2}}[/itex]
    The integration over the 3 angles will give [itex]2\pi^{2}[/itex] and you have to solve now:
    [itex]\int \frac{2\pi^{2}p^{3}dp}{(2\pi)^{4}}\frac{1}{p^{2}}=\frac{1}{8\pi^{2}} \int p dp=\frac{p^{2}}{16\pi^{2}}[/itex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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