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Two square brackets?

  1. Sep 17, 2010 #1
    Dear guys,

    Have you ever met this kind of tensor expression?

    [tex] A_{[a } C_{c]} [/tex]

    That is, indices [tex] a, b[/tex] are anti-symmetric, and indices [tex] b, c[/tex] are anti-symmetric as well. I am confused by this, should I think this expression as: I anti-symmetrise indices [tex] a, b[/tex] first, and then antisymmetrise indices [tex] b, c[/tex]? this would result in

    [tex] \frac{1}{4} (A_{a b} C_{c} - A_{b a} C_c - A_{a c} C_{b} + A_{c a} C_{b}) [/tex]

    But, if I think of this expression by the meaning that I would get a minus sign whenever I exchange [tex] a, b[/tex], as well as I exchange [tex] b,c [/tex]. In this way, what I get should be

    [tex] A_{[ab} C_{c]} [/tex]

    So, which one is correct? I'm really confused...
    Thanks for your help!
  2. jcsd
  3. Sep 17, 2010 #2
    Probably they mean that you antisymmetrize over the indices a and c only, while the index b is left unchanged.
  4. Sep 17, 2010 #3
    Thanks for your discussion.
    But, no, in that case the expression is written as

    [tex] A_{[a|b|} C_{c]} [/tex]

    where the index [tex] b [/tex] is enclosed by two bars, [tex] | | [/tex].
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