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Product of two integrals

  1. Apr 27, 2010 #1

    Hepth

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    Gold Member

    If I have an integral:
    [tex] A = \int \frac{d^d p}{(2 \pi)^d} Z[p][/tex]

    And I want [tex] A^* A [/tex]

    Is it
    [tex] A^* A = \int \frac{d^d p}{(2 \pi)^d} Z^*[p] Z[p] [/tex] ?

    Because the "p" is the same, and really it would be integral 1 times integral 2 times a delta, which should make it just one.

    I don't think its true, and an example in mathematica doesnt work.

    Is there a shortcut to get the product of two integrals to be one?:
    [tex](\int \frac{d^d p}{(2 \pi)^d} Z^*[p])( \int \frac{d^d p}{(2 \pi)^d} Z[p]) =[/tex]

    hmm, the product of two sums...
     
  2. jcsd
  3. Apr 28, 2010 #2

    jasonRF

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    Recall that the variables you integrate over are dummy variables. So you should write
    [tex](\int \frac{d^d q}{(2 \pi)^d} Z^*[q])( \int \frac{d^d p}{(2 \pi)^d} Z[p]) =
    \int \frac{d^d q}{(2 \pi)^d} \int \frac{d^d p}{(2 \pi)^d} Z^*[q] Z[p] [/tex].

    Whether or not you can do something clever with this to make it a single integral depends on the form of [tex]Z[/tex].
     
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