I try to check the calculation that Kaluza and Klein originally did. It is in the first pages of Pope's lecture notes: http://faculty.physics.tamu.edu/pope/ihplec.pdf(adsbygoogle = window.adsbygoogle || []).push({});

I have a few problems with the calculation of the Ricci tensor with spin connection, namely with the inverse vielbeins. The vielbeins are given by the following expressions

\begin{align}

\hat{e}^{a}=e^{\alpha\phi}{e}^{a}

\end{align}

\begin{align}

\hat{e}^{z}=e^{\beta\phi}(dz+A_{\mu}dx^{\mu})

\end{align}

\begin{align}

\hat{E}_A^M\hat{e}_M^B=\delta_A^B

\end{align}

where A,B are the flat indexes in 5d and M,N the curved ones. How can I calculate for example

$ \hat{E}_z^{\mu}$ from this relation? is it correct to use this relation like in the following expressions?

\begin{align}

\delta_a^z =\hat{e}_a^M\hat{E}_M^z=\hat{e}_a^{\mu}\hat{E}_{\mu}^z+\hat{e}_a^{z}\hat{E}_{z}^{z}

\end{align}

Are there any books where I can find more about vielbeins in more than 4d?

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# Vielbein for kaluza-klein

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