# What is a double trace?

1. May 2, 2007

### kauw7

Hello all,

I have recently encountered a tensor which is said to have the property "zero double trace". I am unfamiliar with the concept of a double trace and was hoping someone here could help.

Thanks

2. May 2, 2007

### robphy

What kind of tensor is it? Does it have a specific name?
How many indices does it have?

3. May 2, 2007

### kauw7

I don't think it has a proper name, but it has all the symmetries of the Riemann tensor. It is rank four and the indices run from 0:3.

Thanks

4. May 2, 2007

### Chris Hillman

Iterated contraction

This can only mean, I think, an iterated contraction, e.g.
$${P^{ab}}_{cd} \mapsto {Q^a}_d = {P^{am}}_{md} \mapsto R = {Q^m}_m$$
But as you can see by permuting the indices, there are in general many such double contractions!

Incidently, the obvious guess is that you are reading about the Weyl tensor, aka conformal curvature tensor, which shares all the symmetries of the Riemann tensor but which is also "completely traceless". Did you see the concurrent thread on that object?

5. Dec 12, 2008

### [Matrix]

Is this what everyone else thinks the mysterious 'double trace' must be? I came across it in a paper on the standard model extension by A. Kostelecky and M. Mewes...

Does anyone have any other ideas about what they could be talking about?