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Vielbein for kaluza-klein

  1. Jan 28, 2010 #1


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    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
    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
    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?
    \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}
    Are there any books where I can find more about vielbeins in more than 4d?
  2. jcsd
  3. Jan 29, 2010 #2
    Just fixed the latex for you :)
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