- #1
redstone
- 26
- 0
Homework Statement
Wondering if one particular tensor manipulation is "legal"
Homework Equations
[tex]U^{ij}=\eta_{ab}F^{ia}F^{jb}[/tex]
where F is the electromagnetic tensor, antisymmetric, with zeros on the diagonal
The Attempt at a Solution
So, starting there, is it legal for me to do this?
[tex]U^{ij}=F^{i}_{b}F^{jb}[/tex]
[tex]U^{ij}=\eta^{b}_{i}\eta^{ai}F_{ab}F^{ji}[/tex]
[tex]U^{ij}=\eta^{ab}F_{ab}F^{ji}[/tex]
[tex]U^{ij}=0[/tex]
since,
[tex]\eta^{ab}F_{ab}=0[/tex]
that makes my answer seem to trivial to be the real answer, but I don't see the mistake