Thursday, 12 January 2017

electromagnetism - Tensor product notation



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?




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