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Comma notation in tensor expression?

  1. Sep 5, 2008 #1
    The wikipedia article on Electromagnetic tensor has:

    With the electromagnetic tensor, the equations for magnetism reduce to

    [tex]F_{ \alpha \beta , \gamma } + F_{ \beta \gamma , \alpha } + F_{ \gamma \alpha , \beta } = 0. \,[/tex]

    Can somebody point me to an online reference that explains the comma notation please (or explain directly if not time consuming).
     
  2. jcsd
  3. Sep 5, 2008 #2

    George Jones

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    For example,

    [tex]F_{ \alpha \beta , \gamma } = \frac{\partial F_{ \alpha \beta}}{\partial x^\gamma}[/tex].
     
  4. Sep 5, 2008 #3

    cristo

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    The comma just means partial derivative: so, say, [tex]F_{ab,c}\equiv\partial_cF_{ab}\equiv\frac{\partial F_{ab}}{\partial x^c}[/tex]
     
  5. Sep 5, 2008 #4
    thanks guys. after posting I also found that answer in a different article:

    Covariant_formulation_of_classical_electromagnetism

    Is this well used notation? (it's not that much harder to write a D than a ,)
     
  6. Sep 5, 2008 #5

    cristo

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    Yes, the comma notation is well used: whilst it may not save much time in short expressions like that in the OP, it certainly saves a lot of time in longer expressions. You may also come across a semicolon: this generally means the covariant derivative.
     
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