Talk:Electromagnetic tensor

message: As per my comments on http://en.wikipedia.org/wiki/Electromagnetic_four-potential 
and http://xxx.lanl.gov/abs/physics/0401067 
I believe that the defintion of the vector potential in SI units is incorrrect.
It should be:
: A^a = \left(\frac{\Phi}{c}, \vec{A} \right) 
: A_a = \eta_{ab} A^b = \left( -\frac{\Phi}{c}, \vec{A} \right) 
I will let this stand for comments before editing the page.
:Looks like the inner product η has signature (-,+,+,+) in Wikipedia. It wasn't clear enough when I changed this page. --TxAlien 18:26, 9 December 2006 (UTC)
thread_title:  SI problems? 

message: I proposed that all article is in the SI, including the lagrangian.
The lagragian density for electrodynamics in SI is:
\mathcal{L}=-\frac{1}{4 \mu_0}F^{\alpha\beta}F_{\alpha\beta},\,
i.e., there is the constant \mu_0 in the lagrangian. —The preceding unsigned comment was added by Lseixas (talk • contribs) 17:55, 24 December 2006 (UTC)
replies: text: Sorry for unsigned my comment. Lseixas 00:03, 27 December 2006 (UTC)
thread_title:  All article in SI 

message: In the section The field tensor and relativity, somebody had written:
"The elegance of these equations stems from the simple replacing of partial with covariant derivatives, a practice sometimes referred to in the parlance of GR as 'replacing partial with covariant derivatives'. "
I assume that this is intended to be some form of ironic humor?
Geoffrey.landis 13:49, 17 July 2007 (UTC)
thread_title:  Humor? 

message: In "Relation to classical electromagnetism", I feel like the transition between eq 5 and 6 (just before "That term in the parenthesis is just the field tensor") lacks justification. One problem is that the same indices mu and nu are double-used, both in the Lagrangian density and in the Euler-Lagrange equation. They should really be separate indices, and then only made equal by noting that only the terms in the sum for the Lagrangian which have the same (or switched) indices contribute.  —Preceding unsigned comment added by 71.184.189.66 (talk) 08:08, 11 February 2008 (UTC)
thread_title:  Skipping some steps? 

message: Most of the article uses \partial_{\alpha} for the partial derivaties \frac{\partial}{\partial x^{\alpha}} but in the quantum Lagrangian is written with D_{\alpha}.  I think that these are intended to be equivalent (and if so think the article probably ought to use consistent notation).
Can anybody verify?
Peeter.joot (talk) 17:22, 7 September 2008 (UTC)
replies: text: I thought D_\alpha is meant to be a covariant derivative... ie. D_\alpha = \partial_\alpha + ie A_\alpha --Immer in Bewegung (talk) 22:57, 7 September 2008 (UTC)
thread_title:  quantum Lagrangian. 

message: In the article 
http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism
the matrix of the metric tensor is written:
:F^{\alpha\beta} = \left(
\begin{matrix}
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
\end{matrix}
\right) .
whereas in this article:
::F^{\mu\nu} = \begin{bmatrix}
0 & E_x/c & E_y/c & E_z/c \\
-E_x/c & 0 & B_z & -B_y \\
-E_y/c & -B_z & 0 & B_x \\
-E_z/c & B_y & -B_x & 0
\end{bmatrix}
 
Other than the different stylistic issues, the signs of the electric field coordinates are inverted despite both claiming to be associated with a -+++ metric.  One of them looks wrong.  What I get working out the tensor in terms of the bivector equation:
:
F = E + icB = E^i \gamma_{i0} + \gamma_{0123} c B^{i} \gamma_{i0}
where
:
F^{\mu\nu} = F \cdot \gamma^{\nu\mu}
agrees with the covariant article, but it's fairly easy to get indexes messed up in these tensor expressions, so perhaps somebody familiar with the traditional non-clifford-algebra formulation of the em tensor equations can comment.
Peeter.joot (talk) 12:39, 9 September 2008 (UTC)
thread_title:  Metric tensor definition? 

message: I may be mistaken, but I'm fairly certain that there is a factor of 2 error in the identity:
:: \epsilon_{\alpha\beta\gamma\delta}F^{\alpha\beta} F^{\gamma\delta} = \frac{4}{c} \left( \vec B \cdot \vec E \right)  = \mathrm{invariant} \,
I've worked it out several times, and I think it should be:
:: \epsilon_{\alpha\beta\gamma\delta}F^{\alpha\beta} F^{\gamma\delta} = \frac{8}{c} \left( \vec B \cdot \vec E \right)  = \mathrm{invariant} \,
Hopefully someone is willing to check me on this. Thanks! Also, please forgive me if I'm not following protocol correctly. This is my first time ever editing something on Wikipedia.WikiCamBob (talk) 16:09, 24 February 2009 (UTC)
thread_title:  Factor of 2 Error 

message: Main changes:
* clean up
* add the many missing links that should be there, a reader will have no clue where to read further (will they know that "det" means determinant of a matrix?? will they know what a differential 2-form is??)
* re-word some of the text, it was prosy and hype defeating WP:NPOV, such as
::"Hidden beneath the surface of this complex mathematical equation is an ingenious unification of Maxwell's equations for electromagnetism."......
F = q(E+v×B) ⇄ ∑ici 18:14, 9 April 2012 (UTC)
thread_title:  clean up 

message: An additional sign error appears in the tensor expression for the inhomogeneous Maxwell equation
\partial_{\beta} F^{\alpha\beta} = \mu_0 J^{\alpha}.
Given that we are using the F_{row\, column} convention and the metric (+---), the correct expression should be 
\partial_{\beta} F^{\alpha\beta} = -\mu_0 J^{\alpha}. OR
\partial_{\alpha} F^{\alpha\beta} = \mu_0 J^{\beta}.
Either works and I prefer the latter because of the lack minus sign. I've changed it because it is consistent with the metric used in the rest of this article, and because I've personally made this sign mistake before.
Fastman99 (talk) 02:44, 17 February 2013 (UTC)
thread_title:  Extra sign errors 

message: In a very tiny font, this article indicates that it uses SI units.  I suppose that is fine, but the EM tensor is slightly nicer in Gaussian units, were there are no /c in the E components.  Would it be too much to explain this, somewhere in the article?  Gah4 (talk) 18:56, 10 May 2019 (UTC)
thread_title:  Units