- #1
jdstokes
- 523
- 1
I'm trying to understand how Randall and Sundrum go from Eq. (9) to Eq. (10) in their RS1 paper:
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.
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.