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How to make my equation fancier?

  1. Nov 23, 2014 #1
    I hope I am posting this in the right thread!
    As I was solving a problem in general relativity, my final answer needs to get a little fancier. So my final answer was as follows: $$ (\bar{U}{U})^3 (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) \wedge (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) $$ But if my theta's are equal to one another they will eat themselves out. This mean for example $$(\theta^1 \wedge \theta^1 = 0)$$ So I don't know if using some neat maths trick I can write out my final answer without the need to put a note of what I just wrote. How to make the equation speak for itself?

    Thank you!
  2. jcsd
  3. Nov 23, 2014 #2

    Ben Niehoff

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    Gold Member

    You need to rename some dummy indices in the second factor so that each index is repeated only twice. Then use

    $$\varepsilon_{abc} \varepsilon_{ade} = \delta^{bc}_{de} = \delta^b_d \delta^c_e - \delta^c_d \delta^b_e$$
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