- #1

Mentz114

- 5,432

- 292

[tex]\frac{\partial^2}{\partial_x\partial_y} + \frac{\partial^2}{\partial_x\partial_z} + \frac{\partial^2}{\partial_z\partial_y}[/tex]

I've never seen it until it came up in a field theory context. What can it mean ?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Mentz114
- Start date

- #1

Mentz114

- 5,432

- 292

[tex]\frac{\partial^2}{\partial_x\partial_y} + \frac{\partial^2}{\partial_x\partial_z} + \frac{\partial^2}{\partial_z\partial_y}[/tex]

I've never seen it until it came up in a field theory context. What can it mean ?

- #2

Pere Callahan

- 586

- 1

[tex]\frac{\partial^2}{\partial_x\partial_y} + \frac{\partial^2}{\partial_x\partial_z} + \frac{\partial^2}{\partial_z\partial_y}[/tex]

I've never seen it until it came up in a field theory context. What can it mean ?

Hm, I've never seen it used in any context before. Where did you see it, maybe it's interesting to me, as well.

- #3

foxjwill

- 354

- 0

[tex] \frac{1}{2} \left ( \begin{bmatrix}

0 &1 &1\\

1 &0 &1\\

1 &1 &0

\end{bmatrix} \nabla \right ) \cdot \nabla[/tex]

which kind of reminds me of the scalar triple product

[tex]\frac{1}{2} \nabla \cdot \left ( \begin{bmatrix} 1\\ 1\\ 1\end{bmatrix} \times \nabla \right )[/tex]

- #4

Mentz114

- 5,432

- 292

The operator is half the divergence of a 3D symmetric curl,

[tex]\nabla^{i} \cdot ( s_{ijk}\partial^{j}A^{k})[/tex].

where s is a symmetric permutation operator, which is like the Levi-Civita symbol, but with positive value where the L-C has a negative.( I can't write this in vector notation just now)

I'm not sure it has any physical interpretation. Given that the divergence of the usual curl is identically zero, I thought this thing might mean something.

foxjwill, you are right, I noticed also what you say. I haven't come across that weird matrix in other context.

M

[tex]\nabla^{i} \cdot ( s_{ijk}\partial^{j}A^{k})[/tex].

where s is a symmetric permutation operator, which is like the Levi-Civita symbol, but with positive value where the L-C has a negative.( I can't write this in vector notation just now)

I'm not sure it has any physical interpretation. Given that the divergence of the usual curl is identically zero, I thought this thing might mean something.

foxjwill, you are right, I noticed also what you say. I haven't come across that weird matrix in other context.

M

Last edited:

- #5

Mentz114

- 5,432

- 292

I've realized that this

[tex] \frac{1}{2} \left ( \begin{bmatrix}0 &1 &1\\1 &0 &1\\1 &1 &0\end{bmatrix} \nabla \right )[/tex]

is another way to write the symmetric curl.

Share:

- Last Post

- Replies
- 6

- Views
- 498

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 421

- Replies
- 6

- Views
- 781

- Replies
- 6

- Views
- 361

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 781

- Last Post

- Replies
- 16

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 870

- Last Post

- Replies
- 7

- Views
- 1K