
#19
Mar1405, 02:41 PM

Sci Advisor
PF Gold
P: 2,226

Yes it's the summation convention your missing physicist, remember that matrices are only (limited) representations of tensors,




#20
Mar1405, 03:21 PM

Emeritus
Sci Advisor
PF Gold
P: 5,540

Physicist, you're missing a couple of other things, too.
[tex]\mathbf {A} ^2= \mathbf {A} \cdot \mathbf {A}= A_x^2+A_y^2+A_z^2[/tex] The other thing you're missing is this issue of matrix multiplication. [itex]F^{\mu \nu }F_{\mu \nu }[/itex] does not mean that you are supposed to multiply the matrix representations of [itex]F[/itex] together. It means that you are supposed to sum over the indices, as I described in my last post. If you were supposed to do matrix multiplication, it would be written as follows: [tex] F^{\mu \nu } F_{\nu \lambda } [/tex] 



#21
Mar1405, 03:24 PM

Sci Advisor
HW Helper
P: 11,863

Not really,Tom.What u've written is a 4th rank (2,2) tensor.It doesn't have matrix representation in R^{2}...
Daniel. 



#22
Mar1405, 03:31 PM

Sci Advisor
PF Gold
P: 2,226

No Tom is correcr, but perhaps it's better to treat Matrices as (1,1) tensors, so [itex]F^{\mu}_{\alpha}F^{\alpha}_{\nu} = F^{\mu}_{\nu}[/itex] is the kind of operation that phsyicist is doing.




#23
Mar1905, 04:01 PM

P: 43

Thank you all..
Thanks alot 


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