- #1
spaghetti3451
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The antisymmetric 2-tensor ##F_{ij}## is given by ##F_{ij}\equiv \partial_{i}A_{j}-\partial_{j}A_{i}##
so that ##F_{ij}={\epsilon_{ij}}^{k}B_{k}## and ##B_{i}=\frac{1}{2}{\epsilon_{i}}^{jk}F_{jk}##.
I was wondering if the permutation tensor with indices upstairs is different from the permutation tensor with indices downstairs.
so that ##F_{ij}={\epsilon_{ij}}^{k}B_{k}## and ##B_{i}=\frac{1}{2}{\epsilon_{i}}^{jk}F_{jk}##.
I was wondering if the permutation tensor with indices upstairs is different from the permutation tensor with indices downstairs.