Talk:Electromagnetic four-potential

message: Article expanded. To keep both camps happy, I've used both SI and gaussian units. Mpatel
Might be nice to add the formal solution for the 'retarded potentials' in terms of [j] [phi], (eg Bleaney & Bleaney E&M p283) - not sure my ability with the formula generator is up to that.:-) Linuxlad 16:54, 11 Apr 2005 (UTC)
thread_title: Untitled

message: a Therm noted as A^a = (\phi, \vec A c) isn't a 4-vector - its a quaternionic term. If it would be a vector it would need to get noted as \vec{A^a} = \dots. Anyway, the four-potential is afaik quaternionic. -- MovGP0 10:34, 26 May 2006 (UTC)
thread_title:  vector? 

message: The equations for the electric and magnetic fields that result from a 4-potential are needed on this page.  I may take a shot at doing the edits myself, if nobody beats me to it.
Pervect 20:55, 22 July 2006 (UTC)
thread_title:  E & B fields from 4-potential 

message: There appear to be problems with the SI formulation on this and other pages:
See for instance: http://xxx.lanl.gov/abs/physics/0401067
Also, Griffiths "Introduction to Electrdynamics"
We should have in SI units:
: A^a = (\frac{\Phi}{c},\vec{A})
: A_a = (-\frac{\Phi}{c},\vec{A})
: This gives A^a A_a = |A|^2 - \Phi^2 in SI units
: And, in Gaussian units A^a A_a = |A|^2 - c^2 \Phi^2
This is the same as http://en.wikipedia.org/wiki/Electromagnetic_tensor in the "derivations"
section except for choice of sign conventions.  (It's incompatible with earlier statements on the page).
I will let this stand for comment before making any edits on this and/or other affected pages.
Having received no negative comments, I've fixed up this page & will do the others as time permits.
Pervect 06:40, 30 July 2006 (UTC)
thread_title:  SI problems? 

message: Forgive my ignorance, but could someone define the superscript α?  Also, since α does not explicitly appear in the right side of the equation, a discussion of how the equation varies with α might also be helpful.  Wikimedes (talk) 19:15, 14 October 2010 (UTC)
replies: text: Alpha isn't a quantity as such, but a index that can represent the spacetime dimensions 0,1,2,3. It's standard to use greek letters to imply this, see for example http://en.wikipedia.org/wiki/Einstein_notation. :) 91.106.44.228 (talk) 17:25, 20 February 2011 (UTC)

text: The alpha is implied on the right hand side of the equation where it is equal to zero for the scalar potential and equal to 1,2,3 for the vector potential. Dauto (talk) 18:26, 25 May 2011 (UTC)
thread_title:  Definition of the superscript alpha? 

message: I think it would be very helpful to know why is necessary its introduction. Paranoidhuman (talk) 15:25, 25 May 2011 (UTC)
replies: text: What do you mean? It's an essential part of electromagnetic theory. If you want to understand electromagnetism, than you must introduce the potential. Dauto (talk) 18:11, 25 May 2011 (UTC)
replies: text: But that's not why. That's just shifting the question to a different part of the sentence : it must be introduced because its necessary for an understanding; but why is it necessary? What is it about an understanding that requires it? That's the question.
Or to put it another way, the article should say
*(a) that it is used to define the EM Field Strength tensor
*(b) that maxwell's equations can be compactly written in terms of that tensor
*(c) creating a lagrangian that involves that tensor, some electron fields, and a co-variant derivative of the four-potential, creates 
**(i) The conservation of charge, by Noether's theorem
**(ii) Euler-lagrange equations in the electron fields, that produce the dirac equation, and hence the quantum description of electrons
**(iii) Euler-lagrange equations in the four-potential, that produces half of maxwell's equations
*(d) the other half of maxwell's equations turn up from guage fixing the four-potential
*(e) photons, from quantisation of the EM field strength tensor part of the lagrangian  — Preceding unsigned comment added by 94.196.243.2 (talk) 12:29, 13 March 2016 (UTC)
thread_title: Necessity

message: In the section titled The Lorentz Gauge, the second box (the table following the definition of the D'Alembertian) The SI column has minus signs for the sources, while the Gaussian column has them positive. I don't think that can be right.  — Preceding unsigned comment added by 209.129.16.79 (talk) 03:11, 14 April 2017 (UTC)
thread_title:  Sign error? 

message: Someone has put [clarification needed] tags in the Gauge Freedom section, which is a fair move in my opinion as that section is currently quite obscure. Some thoughts on this below:
- I've added a brief explanation of 'flattening' (aka index lowering) from the point of view of someone who has used tensor algebra for theoretical physics.
- I don't know anything about cohomology, and only a very limited understanding of gauge invariance, so I don't understand the rest of the section. Hopefully someone else can help out here: it sounds like an interesting topic and could do with some clarification.
- Maybe there are more Wikipedia pages that aren't currently linked here (or some good references) which can clarify the notation / theory further.
- Is "Gauge Invariance" a better name than "Gauge freedom"? DigitalHamster (talk) 20:58, 29 December 2023 (UTC)
thread_title:  Clarification of the section on Gauge freedom