What is the significance of square brackets in tensor notation?

[Identity]

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

 

[Matterwave]

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]

 

[Identity]

Ah yes, thanks matterwave, I guess (ab) is the symmetric part then

 

[George Jones]

Ah yes, thanks matterwave, I guess (ab) is the symmetric part then

Yes.

 

[dextercioby]

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.