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Problem with integrals

  1. Oct 1, 2013 #1
    Hi! I've got a problem with an integral. Let's assume we've got something like this:

    R3d3x1R3d3x2R3d3x3R3d3x4P(|x1|)P(|x3|)δ(x1+x2)δ(x3+x4)W(|x1+x2|)W(|x3+x4|)


    xi is a vector
    The "δ" is the Dirac delta.
    P(|x|i) & W(|xi+xj|) are some functions
    I would like to make it looks a bit simpler---I mean get rid of deltas and two integrals. How can I make it?
    Thanks for help and sorry for spelling mistakes!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 1, 2013 #2
    What have you attempted? Do you understand the properties of the delta function?
     
  4. Oct 2, 2013 #3
    if the xi=-xj then δ ≠0.

    R3δ(x)d3x should be equal 1. Well, actually it should looks

    like this:

    -∞δ(x)dx=1

    but it is the same I thing.. This is all I know.
     
  5. Oct 2, 2013 #4
    Okay, also note that [itex] \int \cdots \int f(\vec{x}) \delta(\vec{x} - \vec{x}_o) d^Nx = f(\vec{x}_o)[/itex]. This can allow you to fix some variables.

    My next question is, are we integrating from [itex]-\infty \rightarrow \infty [/itex]? If the variable being integrated is not within the bounds, we can simplify things greatly.

    I must say, it has been awhile since I have done integrals of this form.
     
  6. Oct 2, 2013 #5
    Well, we are integrating it over the entire R3..
    I don't get it. There isn't any function depending on x. there is only P and W that depend on |x| or |xi+xj|

    PS I can't put P and W before the integrals, can I?
    PPS One more thing. There is a integral:
    ∫d3x1
    and let's assume x1=x2+x3 so the d3x1=d3x2+d3x3. So after substitution
    ∫d3x1=∫d3x2+∫d3x3? is it correct?
     
    Last edited: Oct 2, 2013
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