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Calculate the invariant problem

  1. Dec 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate the invariant
    E^{\alpha \beta} E_{\alpha \beta}

    2. Relevant equations

    3. The attempt at a solution
    we apply the metric in this case,
    E^{\alpha \beta} E_{\alpha \beta} = g_{\alpha n} g_{\beta m} E_{n m} E^{n m}

    is that even correct?
  2. jcsd
  3. Dec 10, 2009 #2


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    Homework Helper
    Gold Member

    Re: Metric

    No, that equation is non-sensical...on the lefthandside [itex]\alpha[/itex] and [itex]\beta[/itex] are dummy indices (they are being summed over)...on the righthandside they are free indices and you also have [itex]m[/itex] and [itex]n[/itex] appearing 3 times (which is notational nonsense).

    I assume you are given either [itex]E^{\alpha \beta}[/itex] or [itex]E_{\alpha \beta}[/itex]?
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