- #1
noamriemer
- 50
- 0
Hello!
I need to find the relation between E^{2}-B^{2} and F_{\mu\nu} F^{\mu\nu}
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:
F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...<br /> 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 E^{2}-B^{2} and F_{\mu\nu} F^{\mu\nu}
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:
F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...<br /> and that is not the product I expect it to be...
Could someone explain me how these definitions get along?
Thank you!
