Semi-colon vs nabla notation

  • Thread starter pellman
  • Start date
  • #1
673
2

Main Question or Discussion Point

Is it

[tex]\nabla_\mu\nabla_\nu A^\alpha={A^\alpha}_{;\mu\nu}[/tex]

or

[tex]\nabla_\mu\nabla_\nu A^\alpha={A^\alpha}_{;\nu\mu}[/tex]

?
 

Answers and Replies

  • #2
dextercioby
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The second is the right one.

[tex] \nabla_\mu \nabla_\nu A^\alpha=\left(A^{\alpha}_{~;\nu}\right)_{;\mu}= A^{\alpha}_{~;\nu;\mu} = A^{\alpha}_{~;\nu\mu} [/tex]

To avoid errors, my suggestion is not to use them both at the same time when making calculations.
 
  • #3
CompuChip
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This is one reason I prefer the nabla-notation. (Another is that I often get confused afterwards whether I that little dot over the comma is just a little ink drop or I actually meant to write a semi-colon.)
 
  • #4
673
2
Thanks!
 

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