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About an integral

  1. Jul 17, 2009 #1

    ppg

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    Hi, im a newcomer, and i have a question about an integral shown as follows,

    [tex]\int d^{3}p_{2} \frac{1}{2E_{2}} d^{3}p_{3} \frac{1}{2E_{3}} \delta^{4}(p-p_{2}-p_{3}) p_{3}^{\alpha} p_{3}^{\beta} p_{2}^{\mu}[/tex]

    Is this integral equal to (just considering Lorentz structures)

    [tex]A(p^{2})g^{\alpha\beta}p^{\mu}+B(p^{2})g^{\beta\mu}p^{\alpha}+B(p^{2})g^{\mu\alpha}p^{\beta}[/tex]

    where the coefficients of the last two terms should be the same because of the symmetry of the integral variables [tex]p_{3}^{\alpha} p_{3}^{\beta} [/tex]

    Thank u for ur help!!
     
    Last edited: Jul 17, 2009
  2. jcsd
  3. Jul 17, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    It's been a while since I did such HEP integrals, so I can't give you an answer off the top of my head. But I want to give you a tip, since you have posted the formulas in valid LaTeX code anyway: if you wrap them in tex-tags (put [ tex] at the beginning and [/ tex] at the end, and take out the spaces in both :)) they will be nicely rendered by LaTeX. For inline (i.e. $ ... $) you can replace tex by itex in both tags. That will make your post a lot more readable, probably giving you faster responses as well.

    Quote my message to see the codes used:
    [tex]\int d^{3}p_{2} \frac{1}{2E_{2}} d^{3}p_{3} \frac{1}{2E_{3}} \delta^{4}(p-p_{2}-p_{3}) p_{3}^{\alpha} p_{3}^{\beta} p_{2}^{\mu}[/tex]
    [...] integral variables [itex]p_{3}^{\alpha} p_{3}^{\beta}[/itex].
     
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