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Totally antisymmetric tensor

  1. Oct 11, 2007 #1
    1. The problem statement, all variables and given/known data
    The totally antisymmetric rank 4 tensor is defined as 1 for an even combination of its indices and -1 for an odd combination of its indices and 0 otherwise.

    Is a rank 3 totally antisymmetric tensor defined the same way?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 11, 2007 #2


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    Mmmmmm. Yes! Do you think 4 is special?
  4. Oct 12, 2007 #3

    George Jones

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    The definition is the same, but remember that a cyclic permuation is even/odd iff the number of elements being permuted is odd/even. This sometimes causes confusion when moving moving from 3 to 4 dimensions.
  5. Jan 26, 2011 #4
  6. Mar 30, 2011 #5
    Yes and no, I think the definition here is incomplete. It does not include what happens when you raise and lower an index. The rank 4 anti-symmetric tensor is a psuedotensor, the rank 3 one is a true tensor. So overall no.
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