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Tensor indicies switch

  1. Oct 30, 2008 #1
    Wondering if this is valid to do, if I start with the expression

    [tex] \delta\omega^{u}_{ \singlespacing v} x^v \partial_u [/tex]

    where [itex] \delta\omega [/itex] is an infinitesimal, and [itex] \partial [/itex] a space-time derivative,

    is it still valid to drop and raise the u to obtain

    [tex] \delta\omega_{u v} x^v \partial^u [/tex]

    without involving the metric tensor?
  2. jcsd
  3. Oct 30, 2008 #2


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    Hi waht! :smile:

    Yes, it's just a (double) dot-product:

    [tex] \delta\omega^{u}_{ \singlespacing v} x^v \partial_u [/tex]

    [tex]=\ \delta\omega_{w\singlespacing v}g^u_w x^v \partial_u [/tex]

    [tex]=\ \delta\omega_{w\singlespacing v} x^v \partial_w [/tex] :smile:
  4. Oct 30, 2008 #3
    Thanks Tim, that cleared it up.
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