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Question about 4-vectors/tensors from a complete novice

  1. Feb 28, 2009 #1
    Is any distinction made between an expression like [itex]A^\nu A_\mu[/itex] and one that looks like [itex]A^\mu A_\mu[/itex]? I can justify something like this to myself through some vague hand-waving and mention of a phrase like "just dummy indices," but this isn't convincing even to me...and I'm making the argument!

    If the context matters, tell me, and I'll provide some. Thanks!
     
    Last edited: Feb 28, 2009
  2. jcsd
  3. Feb 28, 2009 #2

    cristo

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    The Einstein summation convention is invoked on repeated indices, so the difference is that A^u A_v is a tensor, but [tex]A^u A_u=\sum_u A^uA_u[/tex] which is a scalar.
     
  4. Feb 28, 2009 #3
    cristo: Thank you. Of course. I should have known that. I could have saved both of us time and effort if I'd recognized it. Guess that's what happens when you don't really know what you're doing.
     
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