- #1

Theraven1982

- 25

- 0

i had a question (as many do on these forums, it appears ;).

I know E_{k}=F_{0k}

I also know B_{k}=(1/2)*(\epsilon_{klm}*F_{lm})

EM field tensor F^{uv} defined as:

(I put tildes (~) into make it more like a matrix form)

0~~~~E_x~~~E_y~~~E_z

-E_x~~~0~~~~-B_z~~B_y

-E_y~~B_z~~~~0~~~-B_x

-E_z~~-B_y~~~B_x~~~0

However, i want to know how i can write the derivative of this tensor:

0~~~~~~~~Dx(E_x)~~~~Dy(E_y)~~~~~Dz(E_z)

-Dx(E_x)~~~~~0~~~~~~-Dz(B_z)~~~~~Dy(B_y)

-Dy(E_y)~~~Dz(B_z)~~~~~~0 ~~~~~~-Dx(B_x)

-Dz(E_z)~~~-Dy(B_y)~~~~Dx(B_x)~~~~~~0

Where Dx means the derivative wrt x.

So what's the derivative of this tensor in algebraic form?

(like d_{p}F^{uv}*epsilon_{puv} )

I hope someone understands what i mean. And i even more hope someone has a solution: eternal gratitude to this person ;).

Thanks in advance,