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Counting independent components

  1. Sep 16, 2010 #1

    haushofer

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    Science Advisor

    Hi,

    I have a question about counting (how difficult should that be ;) )

    I have the set of tensors in D dimensions

    [tex]
    \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\}
    [/tex]

    with the relations

    [tex]
    H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho}
    [/tex]

    [tex]
    T^{\mu}t_{\mu} = 1
    [/tex]

    [tex]
    H^{\mu\nu}t_{\nu} = h_{\mu\nu}T^{\nu} = 0
    [/tex]

    and h and H are symmetric tensors of rank (D-1).

    The question now is: how many independent components does this set of fields constitute? Mathematica gives as answer 1\2D(D+1), the same amount as for a symmetric rank D tensor, but how can I derive this analytically?
     
  2. jcsd
  3. Sep 17, 2010 #2

    haushofer

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    Science Advisor

    Maybe this thread is better off in another place here? :)
     
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