- #1
Theraven1982
- 25
- 0
Hello,
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,
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,