Integral Rewriting: Exploring the Process

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In summary, the conversation discusses the rewriting of a double integral by introducing the variable τ=τ1-τ2. The first integral, which is just beta, eventually cancels out. There is confusion about the absence of beta in the second line and whether it is a typo. The suggestion is made to introduce new variables, τ and μ, to simplify the integral, resulting in the integration over μ becoming trivial. However, the individual is unsure if they have correctly performed the substitution.
  • #1
aaaa202
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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.
 

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  • #2
The first integral is just beta. It eventually cancels out.
 
  • #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.
 
  • #4
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.
 
  • #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?
 

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