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Hodge dual in tensor notation

  1. May 7, 2012 #1
    So I know that the Hodge dual of a p-form [itex]A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} [/itex] in d dimensions is given by

    (*A)^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}} = C\epsilon^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}\mu_1 \mu_2 \cdot \cdot \cdot \mu_p}A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p}
    where C is some number coefficient. I was wondering what the
    constant C is for general p-forms in general d dimensions.
    Also, what is the inverse relation? (I'm guessing it's the
    same as above, but just checking.)
  2. jcsd
  3. May 8, 2012 #2


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    Science Advisor

    C can be anything you like, but if you use C = 1/p! where p is the number of contracted indices, the same formula works for both this formula and the inverse relation.
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