Comma notation in tensor expression?

[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).

 

[George Jones]

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).

For example,

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

 

[cristo]

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

 

[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 ,)

 

[cristo]

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.