noamriemer
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Hello!
I need to find the relation between [tex]E^{2}-B^{2}[/tex] and [tex]F_{\mu\nu} F^{\mu\nu}[/tex]
Actually, I need to use this relation to determine that the first is a scalar.
What I can't understand is how these notations match the formal definition:
If I multiply a matrix by another (same size) I should be receiving another matrix of the same size. Not a scalar...
But if I use the notations I need to use here:
[tex]F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...[/tex] and that is not the product I expect it to be...
Could someone explain me how these definitions get along?
Thank you!
I need to find the relation between [tex]E^{2}-B^{2}[/tex] and [tex]F_{\mu\nu} F^{\mu\nu}[/tex]
Actually, I need to use this relation to determine that the first is a scalar.
What I can't understand is how these notations match the formal definition:
If I multiply a matrix by another (same size) I should be receiving another matrix of the same size. Not a scalar...
But if I use the notations I need to use here:
[tex]F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...[/tex] and that is not the product I expect it to be...
Could someone explain me how these definitions get along?
Thank you!