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Rewriting integral

  1. Jan 14, 2014 #1
    On the attached picture the double integral in the first line is rewritten in the second line by introducting the variable τ=τ1-τ2
    But how exactly does this happen? I simply can't see how two integrals can turn into one.
     

    Attached Files:

  2. jcsd
  3. Jan 14, 2014 #2
    The first integral is just beta. It eventually cancels out.
     
  4. Jan 14, 2014 #3
    I don't understand why it is just beta. There is a Green's function in the integrand. Do you say this because there is no beta in the second line? Because for all I know this could be a typo.
     
  5. Jan 14, 2014 #4

    Office_Shredder

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    Can you do the full substitution where you introduce new variables, say
    [tex] \tau = \tau_1 - \tau_2 \text{ and } \mu = \tau_1 + \tau_2 [/tex]
    to turn a two dimensional integral into a two dimensional integral? You will see the integration over [itex] \mu [/itex] become trivial.
     
  6. Jan 14, 2014 #5
    hmm I'd would say it would give something like the attached, but I don't see any trivial integral. What did I do wrong?
     

    Attached Files:

    Last edited: Jan 14, 2014
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