Akhmeteli

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Dirac equation

Copied from talk:Dirac equation for reference

Forgot to mention - you could ask at Wikipedia talk:WikiProject Physics for expert opinions more quickly than here. Thanks, Maschen (talk) 19:02, 7 October 2012 (UTC)

Talk:Dirac equation#This article has become a disgrace

You might want to see that section in the talk. Forgive me, although regrettably I think your inserted section on the 4th order Dirac PDE is too short to be understandable and be of sufficient interest as it stands:

"In a general case (if a certain linear function of electromagnetic field does not vanish identically), three out of four components of the spinor function in the Dirac equation can be algebraically eliminated, yielding an equivalent fourth-order partial differential equation for just one component. Furthermore, this remaining component can be made real by a gauge transform."

and also seems to interrupt the flow of the prose, because it is a one-off topic compared to the rest of the article. A reader will just read that the Dirac equation can be written as a 4th order PDE for a particular case, but will ask... Why that particular case? Why is it advantageous to gauge transform and make the component real? What new knowledge does it add? Applications? Consequences?... In that talk section, people have stated the result is wrong. I don't know if it is.

I apologize to be so dismissive after all the collaboration you had with Quondum. If possible, and if it really is notable and correct enough, why not create a separate article, even just a paragraph-long stub with a reference (or two)? That's better than nothing and people should be (at least slightly) happier. Best, M∧Ŝc²ħεИ_τlk 18:45, 21 April 2013 (UTC)

Dear Maschen,

Thank you for your message.

First things first. Is my result wrong, as an anonymous contributor states in the Talk section of the Wikipedia article "Dirac Equation"? I replied in that Talk section. Summary of my reply: my result was properly published in a decent peer-reviewed journal. If somebody questions the result, the burden of proof is now on him (her). I just cannot meaningfully answer entirely unsubstantiated critique. I strongly believe my result is correct.

Second, you believe that the section in question "is too short to be understandable and be of sufficient interest as it stands" Let me note that, according to the stats of my site (www.akhmeteli.org), just over the last year, 267 people used the link to my article in the Wikipedia article. That means that the section was interesting enough for them to look at my paper. That also means that they understood enough to get interested. Let me also repeat that I stated in my journal article that its results belong in textbooks, and the referees of the article seem to agree.

I respectfully disagree with the following: "A reader will just read that the Dirac equation can be written as a 4th order PDE for a particular case" - I specifically wrote "In a general case", not "in a particular case". Let me give you an example. One can say: "In a general case, a system of two linear algebraic equations with two unknowns has exactly one solution." On the one hand, one has to add this "In a general case", as this statement is not correct if the determinant of the system is zero, on the other hand, we understand that in some sense it is a very rare case, so as a rule, in the overwhelming majority of cases (a mathematician would say something like "assuming transversality"), the statement is correct. My result is equally general. As for "Why is it advantageous to gauge transform and make the component real? What new knowledge does it add? Applications? Consequences?"... I just cannot copypaste my entire journal article in the Wikipedia article, can I?:-) Let me just quote Schroedinger (please see the reference in my journal article): "One is interested in what happens when [the Klein-Gordon equation] is replaced by Dirac’s wave equation of 1927 or other first-order equations. This and the bearing on Dirac’s 1951 theory will be discussed more fully elsewhere.” Unfortunately, Schroedinger did not wrote anything else on this topic, but I did just what he intended to do - showed how a charged Dirac field can be described with just one real function. So these are truly fundamental results, even if I say that myself.

I respectfully disagree with your suggestion to "create a separate article, even just a paragraph-long stub with a reference (or two)?", as the result would be just buried there - almost nobody would find it there. Furthermore, some people may complain that the result is not notable enough for a separate article. You may be right that the section "seems to interrupt the flow of the prose", but, IMHO, this stylistic problem does not warrant such drastic measure as exclusion of this important result, although they say that "the guillotine is the best cure for dandruff":-) Of course, I would be happy to consider any constructive suggestions to improve style without throwing out the important results.

As for making people happier... We cannot and should not make happy people who want to monopolize the Wikipedia article.

Thank you

Best regards

Akhmeteli (talk) 09:27, 23 April 2013 (UTC)

OK. About the "general/particular cases" I was referring to "if a certain linear function of electromagnetic field does not vanish identically", but then that would be a condition. Also of course you don't have to copy/paste your article into WP, just rephrase into a summary as much as possible. Although these quibbles are not important... I did see your reply too. Best, M∧Ŝc²ħεИ_τlk 11:25, 23 April 2013 (UTC)