# Totally antisymmetric tensor

1. Oct 11, 2007

### ehrenfest

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. Oct 11, 2007

### Dick

Mmmmmm. Yes! Do you think 4 is special?

3. Oct 12, 2007

### George Jones

Staff Emeritus
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.

4. Jan 26, 2011

### jeckster

5. Mar 30, 2011

### pvukovic

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.