I'm trying to understand how Randall and Sundrum go from Eq. (9) to Eq. (10) in their RS1 paper:(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/hep-ph/9905221

I understand that since the extra dimension [itex]\phi[/itex] is periodic, we must have

[itex]\frac{d^2}{d\phi^2}|\phi|\propto \delta(0) - \delta(\phi - \pi)[/itex].

However, I'm not entirely sure why the proportionality constant is 2, i.e, why

[itex]\frac{d^2}{d\phi^2}|\phi|= 2[\delta(0) - \delta(\phi - \pi)][/itex].

I'm assuming that it's related to the [itex]\mathbb{Z}_2[/itex] symmetry of the [itex]S^1/\mathbb{Z}_2[/itex] orbifold, but I'm not sure how to show his.

Thanks.

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# Differentiation on orbifolds

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