A kind of Tensor notation?

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  • #1
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What is meant by things like:

[tex]R_{[abc]}[/tex]

and also things like:

[tex]\nabla_{[a\nabla_b]}[/tex]

Where you have square brackets in the subscript? Thx
 

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  • #2
Matterwave
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It means the anti-symmetric part of that tensor (or, in other words, to anti-symmetrize that tensor).

For example,
[tex]A_{[ab]}=\frac{1}{2}(A_{ab}-A_{ba})[/tex]
 
  • #3
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Ah yes, thanks matterwave, I guess (ab) is the symmetric part then
 
  • #4
George Jones
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Ah yes, thanks matterwave, I guess (ab) is the symmetric part then
Yes.
 
  • #5
dextercioby
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The weighing factor is a matter of convention. For example, some people write

[tex] F_{\mu\nu}=2\partial_{[\mu}A_{\nu]} [/tex]

while others


[tex] F_{\mu\nu}=\partial_{[\mu}A_{\nu]} [/tex]

in case of the e-m fields.
 

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