Talk:Polar form of the Dirac equation

What's the point of this?
This starts out trying to describe a Lounesto classification of spinor fields, but never finishes doing that. It would be nice if we had a clear and coherent article on that but we don't. Most of the manipulations leading up to the punch-line seem reasonable. But the actual "equations in polar form" appear to be singularly ugly and completely unedifying and useless. What's the point? I don't see how this makes anything simpler or more understandable, or easier to solve, easier to understand. The comments about torsion make things only worse. You picked a connection with torsion? What's up with that? Are you trying to do teleparallelism? My overall impression is that this is taking something relatively clear and understandable and is hopelessly obfuscating it. I can't begin to tell you how much I hate obfuscation. I have a vague temptation to prod this for deletion. 67.198.37.16 (talk) 09:09, 22 November 2020 (UTC)


 * Also, is User:Luca-Spinor-Torsion who wrote almost all of this article the same as Luca Fabbri in real life? I'm looking at this article, its a mess, it would be nice if messes weren't created in Wikipedia, and then left for others to clean up. Wikipedia is not meant to be a dumping ground for random stuff. 67.198.37.16 (talk) 09:19, 22 November 2020 (UTC)


 * I mean, seriously, this is ridiculous. What's X? How does X multiply W? When you say "the antisymmetric part of the torsion tensor", are you talking about the contorsion tensor? You define a spin connection but then mix greek and roman indexes throughout; you can't mix greek and roman, it's meaningless garbage when you do. Is nabla supposed to be the covariant derivative? Is it with the Levi-Civita connection, or a connection with torsion? I mean, is that were the W came from, because you split the connection into two parts? Or maybe the nabla includes the affine connection for the electromagnetic field? I really really detest this kind of writing. 67.198.37.16 (talk) 09:36, 22 November 2020 (UTC)

Hi, and yes, I am the Luca Fabbri author of the papers, and I'd like to reply here for clarification: 1. never in the article I talk about Lounesto classification

2. that the equations are "singularly ugly and completely unedifying and useless" is an opinion that I may share or not: I find them easier to read than the Dirac equation, which is written in terms of complex objects (for which there is, of course, no possible reading). I suppose it all depends on the formalism one is used to. There are many well-accepted formalism I find obfuscating, as you say, but I do not dare say they are unclear just cause they seems so to me. Maybe something useful comes out of them. I suspect the first time someone proposed a quaternionic form of Maxwell equations some might have found them terribly obscure. They have later been found to provide new solutions to the Maxwell equations. If you want to delete the article it's fine for me, but there may be many similarly technical articles that should then be deleted too I guess.

3. About torsion, you are right, I specified with more details.

4. about greek and latin indices, well, here I do not understand the comment: you can easily mix greek and roman indices, of course; and if the manifold is such that the full covariant derivative of frames and co-frames is zero, then you can even pass from one type to the other in total equivalence. These are the conditions of soldering. Saying that one cannot implement soldering is the same of saying that GR can't be done on world-valued indices for any coordinate chart... is that what you are saying? I hope not.

IN SUMMARY --- the article here does not contain any error, of course: it is the summary of research paper published in many international journals with peer-review. However, if you think it is too little detailed, and therefore too complicated, to be part of wikipedia, which is after all a general-purpose encyclopedia, I agree. So one solution could be that I can try to make it clearer and with more references. However, some may complain that longer and more detailed articles will be more obfuscating.

Or you can delete it. However, if you do so, I'd require two conditions, if possible. One is to let me know before any other change is made, so to save some work.

And the other would be to have a look around and clean also other pages related to obfuscating material that should not find place here.

(As a side note, since you seem to be someone knowing torsion, try to have a look at the Einstein-Cartan theory on wikipedia: that is a page that needs serious improvement, for example.)

I will be waiting to know what you'd like me to do, whether improve this page or erase it altogether.

Thanks, Luca — Preceding unsigned comment added by Luca-Spinor-Torsion (talk • contribs) 11:41, 22 November 2020 (UTC)


 * OK, well, responding to the above:


 * 1. The first 1/2 or 2/3rds of this article are very similar to what one would write for an article on Lounesto classification, it would be nice if someone knowledgable wrote an article on that.
 * 2. Wikipedia articles are not supposed to be about you opinions, they are supposed to be written for the readers, to enable the readers to understand the material. To explain the material to the readers. If you do not understand the Dirac equation when it is written in it is usual notation, that suggests you do not understand the Dirac equation in any notation at all ... and therefore should not be writing Wikipedia articles about it.


 * 4. No, you cannot mix greek and roman indexes. If you don't understand this ... well, I don't know where to even begin to explain how this is just plain wrong. It tells me you do not understand what a vierbein is, or how to use it. Which means you don't know what a spin connection is, or how to use it.


 * Based on your answers, I will prod this article for deletion, because I have no reason to believe that the last 1/3rd is correct in any way, shape or form. I invite you to start a new article on the Lounesto classification, for which the first 2/3rds of this article would be an OK introduction. 67.198.37.16 (talk) 19:36, 22 November 2020 (UTC)

Thanks for the answers. Let me reply back, in order:


 * 1. Agreed.


 * 2. Agreed too, but I did not have the impression it was my opinion. And by the way, I understand the Dirac equation, have a look at https://inspirehep.net/authors/1026887 for the list of all my works, all peer-reviewed, on the Dirac equation. What I was referring to was the space-time algebra formalism, that uses quaternionic forms. The idea of the polar form is opposite: that is converting every quantity in terms of real functions.


 * 4. yes, come on, you can have a notation with both latin and greek indices, the first related to active Lorentz transformations and the second to passive diffeomorphism; you can even pass between the two with a frame, or tetrad, or vierbein, and if these are compatible with the differential structure you do the passage in full equivalence. Just take the spin connection: it has two greek and one latin index. See the link https://inspirehep.net/authors/1026887 about all the papers I have in GR with tetradic formalism and spin connection.


 * The article is a summary of a formalism that has been published in a dozen of peer-reviewed papers on international journals whose impact factors are among the highest in physics: it is correct. If you want to delete the article based on lack of utility for wikipedia users I understand and it is fine by me. But if you delete it because it is meaningless, that is if you put it on science, then I'd like you to also go see my papers and tell me there where errors are. If you find them I will be greatly thankful to you. If you do not, then you have no reason to believe what is written here is incorrect. I do not want to sound disrespectful, but here we are comparing results contained in a dozen peer-reviewed papers against your unchecked suppositions. You know the Lounesto classification, you must be a good physicists. I am sure you agree that this is not the way science works.

P.S. By the way, is it possible to know to whom I am talking? It would be great to have a way to establish a common ground. Thanks

— Preceding unsigned comment added by Luca-Spinor-Torsion (talk • contribs) 22:21, 22 November 2020 (UTC)