In the image there is a tensor product:
$$F_{\mu\nu}F^{\mu\nu}=2(B^2-\frac{E^2}{c^2})$$
It's about how this operation on the co- and contravariant field strength tensors can give one of the invariants of the electromagnetic field.
I've tried it and it's actually the double inner product, F_lower(row,column)*F^upper(column,row) summed over all rows and columns
$$F_{\mu \nu}F^{\nu \mu}$$
Is this the way I would write it with subscript summation?
How did it come?
No comments:
Post a Comment