Template talk:Editnotices/Page/Mathematical descriptions of the electromagnetic field

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This template refers to part of the differential geometry formulation used for electromagnetism. At one point the Maxwell's equations article included this formulation, after a rewrite [1][2] this content (which the edit notice is referring to) was moved to Maths of EM field.

This edit notice should be moved to Template:Editnotices/Page/Mathematical descriptions of the electromagnetic field where it applies, it is irrelevant in Maxwell's equations now. z = z² + c 09:45, 17 July 2012 (UTC)[reply]

Done But the edit notice needs to be greatly cleaned up. Use {{editnotice}}, clarify what "the formula below" is referring to or otherwise reword it to make sense, put the formulas in <math>, and so on so it's easier to read. Anomie ⚔ 16:44, 18 July 2012 (UTC)[reply]

By my own judgement this would be the reworded notice:

4-current as 1-form and 3-form

Please note: the four-current J is defined as a 3-form here. ~~Please do not change d*F = *J to *d*F = J (LHS 1 form, RHS 3 form).~~ Please leave Maxwell's equations as

d\,{\star F}=J,dF=0

. In much of the literature J is defined as a 1-form (hodge star of our J) but the three-form version is much nicer (e.g., J is closed rather than co-closed) and much closer to physical intuition (e.g., for a spacelike 3-dimensional region V,

\int _{V}J=

total charge in V).

but I'm not proficient in differential geometry (yet) so I asked here just to make sure it makes sense. I asked the original creator (user:Koavf) but he was not sure either. Please wait before transplanting this with the current version. Thank you for moving it. z = z² + c 19:39, 18 July 2012 (UTC)[reply]

If

J

is a 3-form, then the correct formula is

J=d(\star F)

, but neither of the above. It is only

d(\star F)

which is a (not necessarily zero) 3-form, because

dF=0

, and Hodge duals to 3-forms are 1-forms in 4-space. Incnis Mrsi (talk) 07:50, 19 July 2012 (UTC)[reply]

d\star F=J

is the one in the article, the notice was supposed to indicate not changing some other formula to

\star d\star F=J

.

Lets just simplify it by writing

"leave Maxwell's equations as

d\star F=J,dF=0

"

in place of

"Please do not change

d\,{\star F}={\star J}

to

{\star d}\,{\star F}=J

(LHS 1 form, RHS 3 form)."

Agreed?z = z² + c 08:15, 19 July 2012 (UTC)[reply]

I tried fixing some of the article maths of EM field which includes both conventions (current as a 3-form and a 1-form), so ~~I'm not sure if this notice is even needed anymore...~~ this template notice may as well be deleted since the article now explains what the notice says anyway... z = z² + c 08:43, 19 July 2012 (UTC)[reply]

Do not say "d\star F", because LaTeX and MathJax think \star is a binary operator and resulting spacing is confusing. You can say "d\,{\star F}":

d\,{\star F}

if you dislike parentheses. Incnis Mrsi (talk) 09:07, 19 July 2012 (UTC)[reply]

Sorry I'll fix that. z = z² + c 09:28, 19 July 2012 (UTC)[reply]