10
votes
3answers
1k views

What does the dual of a tensor mean (e.g. dual stress tensor in relativistic ED)?

I know what the dual of a vector means (as a map to its field), and I am also aware of of the definition a dual of a tensor as, $$F^{*ij} = \frac{1}{2} \epsilon^{ijkl} F_{kl}\tag{1}$$ I just don't ...
2
votes
0answers
483 views

de Sitter and anti de Sitter metric

Is the following correct for the distance $d$ from the origin $(0,0)$ to point $(t,x)$ in the 2-dimensional de-Sitter and anti de-Sitter spaces? Here, $t$ is time and the distance may be called the ...
22
votes
4answers
5k views

Are matrices and second rank tensors the same thing?

Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified: 1-Are matrices and second rank tensors ...