# A kind of Tensor notation?

## Main Question or Discussion Point

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

## Answers and Replies

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

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

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

George Jones
Staff Emeritus
Gold Member
Ah yes, thanks matterwave, I guess (ab) is the symmetric part then
Yes.

dextercioby
Homework Helper
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.