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I Levi-Civita: very small problem, need two steps explained

  1. Sep 23, 2016 #1
    Hi all,

    kLW43Jw.png

    Can someone explain me the last two steps?

    I don't know why suddenly there is a term with only two indices, and then in the last step you do something distributive and again three indices.

    Thanks in advance
     
  2. jcsd
  3. Sep 23, 2016 #2

    Orodruin

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    Obviously indices are missing in the middle step as well as a definition of what D is and what properties it has. The latter is probably in the text you are quoting but we have no way of knowing this and it is important in order to be able to help you.
     
  4. Sep 23, 2016 #3
    Hi,

    Here is the complete exercise and solution from Zangwhil Modern Electrodynamics. Since my question is about the levi-civita symbol, I thought it would be better to post it here since it is a tensor.

    So in the step e(ijk) D(jk) = e(ijk)D(jk) + e(kj)D(kj)

    So The e(kj)D(kj) part is wrong and it should be e(ikj)D(kj) or e(kji)D(kj) ? And since the other terms ( e(ijk) D(jk) )cancel since they are equal, this e(ikj)D(kj) or e(kji)D(kj) term should be zero, why is this?


    The very last step is just swapping again an index so it turns out to be negative and then you can pull the symbol out, so I think the last step I understand (if it's indeed the case if an index was missing in the former step)

    i9vnbM2.png
     
    Last edited: Sep 23, 2016
  5. Sep 23, 2016 #4

    Orodruin

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    The second to last step should be
    $$\frac 12 (\epsilon_{ijk} D_{jk} + \epsilon_{ikj} D_{kj}).$$
    Note the factor of one half. There should also be a factor of a half in front of the last expression.
     
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