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LeviCivita symbol 
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#1
Jan1512, 09:46 PM

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 [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! 


#2
Jan1612, 09:29 AM

Sci Advisor
P: 1,258

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. 


#3
Jan1612, 09:37 AM

P: 107




#4
Jan1612, 11:03 AM

Sci Advisor
P: 896

LeviCivita symbol
Lorentz Transformation, or Leprous Tyrannosaurus. I think here the first one is ment.



#5
Jan1612, 07:35 PM

P: 107




#6
Jan1612, 08:18 PM

Emeritus
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PF Gold
P: 9,346



#7
Jan1612, 08:57 PM

P: 107




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