- #1
praharmitra
- 311
- 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
[tex]
(*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}
[/tex]
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.)
[tex]
(*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}
[/tex]
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.)