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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Levi-Civita symbol

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**