- #1
mrentropy
- 9
- 0
Hi all,
Quick question I haven't been able to find the answer to anywhere:
Can I use exterior calculus for symmetric tensors?
I'm familiar with the exterior calculus approach to things like Stokes's theorem and Gauss's law, but that's vector stuff. It seems to me the only tensors in exterior calculus are anti-symmetric tensors. This is fine. I understand the wedge product, so this makes sense.
The problem is my tensors aren't anti-symmetric, they're symmetric. I do lots of things with rank-2 symmetric tensor fields in flat space. Perfectly pedestrian things like the viscous stress tensor in a fluid, the stress in a sold, and the Maxwell stress; all of this is nonrelativistic BTW.
So is exterior calculus totally useless for what I do, or am I missing something?
Thanks,
Peter
Quick question I haven't been able to find the answer to anywhere:
Can I use exterior calculus for symmetric tensors?
I'm familiar with the exterior calculus approach to things like Stokes's theorem and Gauss's law, but that's vector stuff. It seems to me the only tensors in exterior calculus are anti-symmetric tensors. This is fine. I understand the wedge product, so this makes sense.
The problem is my tensors aren't anti-symmetric, they're symmetric. I do lots of things with rank-2 symmetric tensor fields in flat space. Perfectly pedestrian things like the viscous stress tensor in a fluid, the stress in a sold, and the Maxwell stress; all of this is nonrelativistic BTW.
So is exterior calculus totally useless for what I do, or am I missing something?
Thanks,
Peter