What is the significance of square brackets in tensor notation?

[Identity]

What is meant by things like:

$$R_{[abc]}$$

and also things like:

$$\nabla_{[a\nabla_b]}$$

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,
$$A_{[ab]}=\frac{1}{2}(A_{ab}-A_{ba})$$

 

[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

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

while others$$F_{\mu\nu}=\partial_{[\mu}A_{\nu]}$$

in case of the e-m fields.