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4-vectors and tensor algebra

  1. Jul 14, 2009 #1
    How would you write the following using index-notation?

    [tex]s \cdot F \cdot u[/tex]

    Given that [tex] s = (s^0, \vec{s}) [/tex] and [tex] u = \gamma(1, \vec{v}) [/tex] are 4-vectors;
    [tex] F [/tex] is a skew tensor of components [tex] F^{ik} [/tex] indicated as [tex] F = - ( \vec{F}^t, \vec{F}^s ) [/tex], [tex] \vec{F}^t= \left\{F^{0 \alpha}\right\} [/tex], [tex] \vec{F}^s = \left\{F^{\beta \gamma}\right\} [/tex], with [tex] \alpha, \beta, \gamma = 1,2,3 [/tex];
    the dot between symbols indicates a contraction of neighboring indices with the metric tensor (+ ---).
     
  2. jcsd
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