Comma notation in tensor expression?

1. Sep 5, 2008

Peeter

The wikipedia article on Electromagnetic tensor has:

With the electromagnetic tensor, the equations for magnetism reduce to

$$F_{ \alpha \beta , \gamma } + F_{ \beta \gamma , \alpha } + F_{ \gamma \alpha , \beta } = 0. \,$$

Can somebody point me to an online reference that explains the comma notation please (or explain directly if not time consuming).

2. Sep 5, 2008

George Jones

Staff Emeritus
For example,

$$F_{ \alpha \beta , \gamma } = \frac{\partial F_{ \alpha \beta}}{\partial x^\gamma}$$.

3. Sep 5, 2008

cristo

Staff Emeritus
The comma just means partial derivative: so, say, $$F_{ab,c}\equiv\partial_cF_{ab}\equiv\frac{\partial F_{ab}}{\partial x^c}$$

4. Sep 5, 2008

Peeter

thanks guys. after posting I also found that answer in a different article:

Covariant_formulation_of_classical_electromagnetism

Is this well used notation? (it's not that much harder to write a D than a ,)

5. Sep 5, 2008

cristo

Staff Emeritus
Yes, the comma notation is well used: whilst it may not save much time in short expressions like that in the OP, it certainly saves a lot of time in longer expressions. You may also come across a semicolon: this generally means the covariant derivative.