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How to deal with this equation involving a plus/minus term

  1. Mar 30, 2015 #1
    Hey guys,

    So I'm reading a textbook which has the following equation:

    [itex]\dot{X}^{-}\pm X^{-\prime}=\dfrac{1}{4\alpha' p^{+}}\left( \dot{X}^{I}\pm X^{I\prime} \right)^{2}[/itex].

    Please note that the [itex]+,-,I[/itex] are indices. Then the author says:

    [itex] \dot{X}^{-}= \dfrac{1}{4\alpha' p^{+}}\left( \dot{X}^{I}\dot{X}_{I}+X^{I\prime}X_{I}^{'} \right) [/itex]

    where the repeated up and down index is using Einstein's summation convention.

    I have no idea how you can get this equation from the first one...can someone explain please?

  2. jcsd
  3. Mar 31, 2015 #2


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    What happens if you write the first as two equations?
    One with +, the other with -. Expand their right hand sides. Then add...
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