# Levi-Civita symbol

by qinglong.1397
Tags: levicivita, symbol
 P: 107 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. Then, in the 2nd paragraph, the product $$e^{iklm}e^{prst}$$ is a tensor of rank 8 and it is a true tensor! Why? We know that $$e^{iklm}$$ does not change sign when one of the coordinates changes its sign. Either does $$e^{prst}$$. 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!
 Sci Advisor P: 1,261 A pseudotensor has the determinant of the LT included in its transformation. This gives a minus sign compare to the transformation of a true tensor. If a pseudotensor is combined with another pseudotensor, the determinant is squared and always gives +1.
P: 107
 Quote by clem A pseudotensor has the determinant of the LT included in its transformation. This gives a minus sign compare to the transformation of a true tensor. If a pseudotensor is combined with another pseudotensor, the determinant is squared and always gives +1.
What does LT stand for? Thank you!

 Sci Advisor P: 912 Levi-Civita symbol Lorentz Transformation, or Leprous Tyrannosaurus. I think here the first one is ment.
P: 107
 Quote by haushofer Lorentz Transformation, or Leprous Tyrannosaurus. I think here the first one is ment.
Should be the first one. Is the second one an English name?
Emeritus