# Rewriting integral

1. Jan 14, 2014

### aaaa202

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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• ###### integral.png
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2. Jan 14, 2014

### dirk_mec1

The first integral is just beta. It eventually cancels out.

3. Jan 14, 2014

### aaaa202

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. Jan 14, 2014

### Office_Shredder

Staff Emeritus
Can you do the full substitution where you introduce new variables, say
$$\tau = \tau_1 - \tau_2 \text{ and } \mu = \tau_1 + \tau_2$$
to turn a two dimensional integral into a two dimensional integral? You will see the integration over $\mu$ become trivial.

5. Jan 14, 2014

### aaaa202

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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Last edited: Jan 14, 2014