I am reading Landau and Lifgarbagez's Classical Theory of Fields, 4th edition. In the beginning of page 18, the completely antisymmetric unit tensor is said to be a pseudotensor, because none of it components changes sign when we change the sign of one or three of the coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

Then, in the 2nd paragraph, the product [tex]e^{iklm}e^{prst}[/tex] is a tensor of rank 8 and it is a true tensor! Why?

We know that [tex]e^{iklm}[/tex] does not change sign when one of the coordinates changes its sign. Either does [tex]e^{prst}[/tex]. Then the product does change its sign either. How could it be possible that the product is a true tensor?

I totally cannot understand. I need your help, your hints. Thank you!

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# Levi-Civita symbol

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