Talk:Dirac equation/Archive 2

Two kinds of Dirac field
There's an important subtlety to the Dirac equation that I don't think this article captures. Historically, Dirac introduced his equation as a relativistic version of Schrödinger's equation, with the wave function interpreted as a quantum amplitude giving a probabilistic description of fermions. The current version of this article does a pretty good job of describing this. But the Dirac field has a completely different significance in Quantum Field Theory, in which it is not a quantum amplitude but rather something akin to a classical field with a quantum description as a field operator. This is described briefly at the article on fermionic fields. I am not sure how best to introduce or describe this distinction in a way that works with this article, but think it's important to do so. Any other thoughts on this?-Dilaton (talk) 19:18, 8 February 2012 (UTC)
 * You sound like you're talking about the Schroedinger picture where the time-dependent quantum weirdness (wave behavior) goes into the wave equation, vs. the Heisenberg picture where the the fields are classical and the quantum weirdness (the wave-nature) and time-dependence is put into the operators. Any quantum equation can be expressed with either picture, including the Dirac one. They are mathematically equivalent, but sometimes one picture is easier to use and sometimes another. S  B Harris 19:48, 8 February 2012 (UTC)
 * FYI the Schrödinger equation is not a (spacial) probabilistic description too. It is Copenhagen interpretation which is. Incnis Mrsi (talk) 19:26, 8 February 2012 (UTC)


 * I think Dilaton is talking about second quantization. In QFT, fields aren't at all like wavefunctions - they're like classical variables that get quantized.  They're the things the wavefunction is a function of.  In QFT you compute the probability amplitude as a function of the configuration of fields, just as in QM you compute the probability amplitude as a function of (say) the position x.  Put yet another way, in QFT the path integral is over fields configurations, while in QM it's over position.


 * So Dilaton is correct, but it's not going to be easy to explain to a non-specialist.  Waleswatcher  ( talk ) 14:21, 10 February 2012 (UTC)


 * In QFT you can actually use either formalism mentioned above. The Heisenberg picture is more often used in QFT because it goes more naturally with the Lagrangian treatment than the Hamiltonian treatment (what Schroedinger introduced for QM), and QFT is more often formulated in Lagrangian terms. The Klein-Gordon equation (for example) can be written for classical fields (provided they are bosonic) and then quantized just once (what is sometimes called second quantization, but since this is quantization of the field, if you start with a free-field equation it really only needs doing once). This can be done using either the Schroedinger formalism where the operators are time-independent, or the Heisenberg one where the operators are time-dependent (this is the more familiar treatment in QFT but not the only one). The solutions are the same, provided some assumptions are made about what the answers mean. I have a QFT text (Peskin and Schroeder) that does this in Chapter 2. The same is true of the Dirac equation and fermionic fields. THIS wiki article treats the Dirac equation with the Schroedinger operator formalism, but in QFT the same equation looks somewhat different because it is set up with Lagrangians and Feynman propagators, in order to more easily quantize fields for interacting particles. The path-integral formulation is Lagrangian and so you only see it represented in what we call the Heisenberg picture, but in theory it could be done the other way (as the above text demonstrates when they introduced QFT with the Klein-Gordon equation applied to "free fields" (no interacting or bound particles). In any case, to address the question above, field quantization ("second quantization" of QFT) is already there to be used with either type of operator (time-independent or time-dependent) with the Dirac equation (or any relativistic equation)-- it's not something new, that Dirac invented. And yes, it's not discussed much here because this article is about the development of the Dirac equation, not its later use in QFT, where rewriting it as a quantum Lagrange-Euler equation makes it look different. S  B Harris 17:32, 10 February 2012 (UTC)


 * With respect, we're not talking about Schrodinger versus Heisenberg pictures here. That's simply a question of whether you put the time dependence into the operators or the state, it's a fairly trivial change.  What's at issue here is that Dirac fields (and scalar fields and vector fields and every kind of quantum field) are not probability amplitudes.  They aren't wavefunctions at all, they aren't anything like the "psi" in non-relativistic quantum mechanics.  They're actually like the "x" in quantum mechanics.  So the Dirac equation is on a very different footing from the Schrodinger equation - it's more closely analogous to Newton's equation F=m x dot dot than it is to the (better) "quantum-state vectors in Hilbert space", we still are referring to probability densities in the DE, just as we are in the Pauli equation that the DE reduces to in the low-energy limit. And indeed, both DE and Pauli equation reduce to the Schroedinger equation (SE) at low energy, and if there is no external field that makes spin-states non-degenerate. You've said the SE has a psi that isn't like the psi in Dirac. But how can one equation reduce to another in some limit, if it's not talking about the same mathematical object? At what point does this magic happen? Finally, if Dirac's psis are not about proability density (for particle location or any other observable), why did Dirac sweat so much about making the sum of them unitary (something only important in figuring probability amplitudes of observables)? The texts are full of ordinary psi solutions of the Dirac equation (DE). I'm looking at one for an electron AT REST. As a spinor it has four parts, each of them a simple exponential. Now look, I'm claiming no expertise on this issue, but I have a lot of texts written by experts, and I read the notation well enough to know what they are saying at least some of the time (and if not, I can usually tell). Yes, it's quite true Schrodinger equation.  In fact, the wavefunction of any QFT satisfies the standard Schrodinger equation in the standard form H psi = i hbar psi dot, not the Dirac or Klein-Gordon equation - but as Dilaton points out, that psi has little to do with the Dirac field (it's a functional of the Dirac field).  Waleswatcher  ( talk ) 05:01, 11 February 2012 (UTC)


 * It does look like the article needs to be re-written in places. For one thing, it refers to the Dirac psi as a wavefunction, which is very bad notation (that may be what Dirac thought it was at first, but that's not what it actually is).  I notice that the article on fermionic fields is better.   I'll take a shot at this article in a few days if no one else does first.   Waleswatcher  ( talk ) 13:59, 11 February 2012 (UTC)

It seems a bit odd to be arguing with somebody who thinks that Dirac thought his psi's (or columns of psis) were wavefunctions, when they really wasn't. I would think Dirac could tell a function from an operator. Whether we call these psis "wavefunctions" or that when QFT methods are invoked, the fields are quantized with creation and annihiliation operators-- that's almost the definition of QFT's approach. But it's a separate procedure and it's not "in" the DE or part of it. Rather it must be done as a second and deliberate step, and the DE "forces" it (or encourages it) more than other equations, because if you don't do it, you end up solving the DE for one-electron, producing all the odd effects like negative-energy states, Zwitterbewegung, Klein paradox behavior, and so on. But this is the fault of QM plus relativistic energies, not the DE itself (again, since low energies the DE becomes the Pauli, etc, obviously this stuff is not "in" the Dirac EQUATION). The DE might be said to predict a small amplitude for ONE positron for that one electron (if read correctly), but not an infinite number of both (that idea came out of Dirac's imagination, not his equation). The problem is not in the DE itself, but in the fact that classical QM and relativity are not compatible without an infinite number of particles in every problem, which is exactly what QFT presumes. One of the reasons to create the creation/annihilation operator formalism of QFT has nothing to do with the DE, because it applies just as well to the Schroedinger equation, although with minimal impact when slow particles are treated. But one of my texts (Peskin and Schroeder) has a cute section in chapter 2 where they look at the "classical" QM probability of a particle going from x to x1 faster than light. Even using relativistic expressions for momentum and energy, that probability turns out to be positive (but small) for a particle to "tunnel" outside its own light-cone and thus violate relativistic causality. The only prescription for fixing this, is to create antiparticles that propagate also in a way to cancel all probabilities of observable particles to appear outside their light-cones. But this is not a problem only "in" the Dirac equation and it really has no place in an article on the DE per se. It appears as a problem for any QM equation describing a single particle and a classical (non-quantized) field. QFT, with all of its infinite-particle-pair soup instead of the classical field, is the only prescription to fix it. That is not Dirac's fix (who instead invented a Dirac sea that is, again, not implicity in his equation and represents the vacuum, not things like the EM field), that is QFT's fix (where something like the Dirac sea appears by operator magic, out of the vacuum OR any field). And to answer the question above, that is why the Dirac field looks different in QFT formalism. All fields look different-- not just Dirac's. This infiniite number of particles that come from these operators and various fields can only be shown to provide unitary probability densities for observables, after renomalization, which Dirac certainly never attempted. Dirac famously asked Feynman in a seminar in about 1947, if Feynman's new theory for QED was "unitary." Feynman didn't (at that time) even know what the word meant. But it took some time to show that QFT theories of various types were unitary, and that was why QED in complete form came a generation after the Dirac equation. And one of the reasons why Dirac himself didn't invent it. S B Harris 19:32, 12 February 2012 (UTC)
 * Dirac equation is indeed an equation, not a physical theory. These are articles like fermionic field where such things as $n$-particle states, creation operators and observables, should be explained in details. When doing such improvements, please, take a look on a discussion at Talk:Quantum superposition, this is an important point (in distinguishing fields from wave functions) too. Incnis Mrsi (talk) 15:21, 12 February 2012 (UTC)


 * "Whether we call these psis "wavefunctions" or (better) "quantum-state vectors in Hilbert space", we still are referring to probability densities in the DE" - Again, from a modern point of view the ψ in the Dirac equation is neither a wavefunction nor a vector in Hilbert space, and its square (with the gamma 0) is not a probability density (it's a charge density or mass density, depending on what you multiply it by). The Dirac field is an operator.    As for why the Dirac equation reduces to the Schrodinger equation in the NR limit, it's because the Dirac field acting on the vacuum creates a single particle state, and that is a vector in the Hilbert space.  Because the field satisfies the Dirac equation, so does that state.  So I suppose the ψ in the Dirac equation can be interpreted as representing the state one gets after acting on the vacuum once with a Dirac field, but that's not what the notion ψ (with no bracket) usually refers to in modern treatments.  In case you simply don't believe me, google brought me a very reliable online source, notes from David Tong (a full professor at Cambridge U. and among the world's experts on quantum field theory).  http://www.damtp.cam.ac.uk/user/tong/qft/five.pdf Here's a quote:
 * Let’s pause our discussion to make a small historical detour. Dirac originally viewed his equation as a relativistic version of the Schrodinger equation, with ψ interpreted as the wavefunction for a single particle with spin.....This is a very diﬀerent viewpoint from the one we now have, where ψ is a classical ﬁeld that should be quantized.
 * It's possible that this is too technical/subtle of a distinction to try to make in a wikipedia article. And I suppose there's an issue as to whether we want to describe the Dirac equation as Dirac thought of it, or whether we want to describe the Dirac equation as it's taught in modern quantum field theory courses.  I'm not sure of the answer to that.   Waleswatcher  ( talk ) 02:11, 20 February 2012 (UTC)

Well, both. As long as the article doesn't become a chapter of a QFT textbook and concentrates more on the Dirac equation than anything else (hence title) its all fine. The article does state the version proposed by Dirac, and later in the article everything becomes advanced. I see no problems with your addition of "fermionic fields", but I have come across the terminology that its a "4-component spinor wavefunction", in a few of the sources given in the article (and cited). Anyway thanks for the tweaks. =)

I don't know QFT inside out (yet - will some day...) so I will not become too involved in the terminology, or even the article anymore. Just thought to add my answer. -- F = q(E + v × B) 13:41, 20 February 2012 (UTC)


 * OK, that's very reasonable. I think the best course of action is probably to have a small section describing the intellectual history of how Dirac's ψ has been interpreted over the years.  That will make it less important how it's referred to in the rest of the article.  But writing such things in a way that's both correct and comprehensible to a general reader is extraordinarily hard.   Waleswatcher  ( talk ) 14:50, 20 February 2012 (UTC)


 * Indeed its hard to write/edit maths/physics articles so laypeople can understand them. Its the solution to the equation - so there is nothing wrong with the inclusion. The only boundary condition is not to talk too much about quantum fields, even if Dirac's theory did activate much of QFT. Anyway go for it - in the Background and development section. =) -- F = q(E + v × B) 16:43, 20 February 2012 (UTC)


 * On second thought I will come back to this breifly. A heading or two will be added in the properties section, and once again will try to shorten the length of the initial description of probability current and this will be moved into the properties subsection Adjoint spinor and conservation of probability current. It still somehow seems detracting, and not 100% relavant (perhaps ~60%, not so sure). Anyone who disagrees may revert. -- F = q(E + v × B) 21:52, 20 February 2012 (UTC)

It is good to see this issue being taken seriously, and to see the improvements. Maybe there is hope. I'll see what I can do. Sorry if I step on any toes in the process.-Dilaton (talk) 19:55, 23 February 2012 (UTC)


 * Most of the edits were positive definite. =) Although I disagree with the removal in this edit . As I said way up above, I tried everything to make the index notation as clear as possible - why did you not think so? I'm not fussed; it doesn't matter either way - just asking.


 * Also why did you remove the subsection in this edit instead of merging with the Square root of the KG equation section? If anything the larger section (still standing) should be cut down and merged into that section. Again - I'm not going to be too involved (actually have no time either - unfortunately procrastinating as usual here on wikipedia instead of uni work), simply wondering.--  F = q(E + v × B) 12:43, 25 February 2012 (UTC)


 * Let's see... for the first edit you mention, the main problem with the removed text was that it referred to some of the Dirac matrices as contravariant vectors. But the Dirac matrices are constants, and these indices are labels. It is only when one contracts with a flat vierbein that one can write the Dirac matrices with the coordinate indices of a contravariant vector; but this is a special case, and so not a good habit. Also, a contravariant vector over a four manifold usually has four components, not three, so that's another confusing aspect of this expression. That said, I didn't have a huge problem with it -- just thought it was more confusing than helpful. For the second edit, the expressions seemed completely redundant compared to those already in the "square root of the KG equation section." The existing KG section is rather painfully long and explicit though, so maybe some sort of merge can be done, I just didn't immediately see how. Saying something succinctly after it's already been said verbosely does not make the result more succinct.-Dilaton (talk) 19:14, 25 February 2012 (UTC)
 * Great move Dilaton, you removed a succinct exposition and left the verbose, "rather painfully long", one. Fantastic work! Science should be complicated.  Obfuscate the world.  Fuck everybody. -- cheers, Michael C. Price talk 19:35, 25 February 2012 (UTC)
 * Michael, I did like the succinct version, but I suspect it's too compact for most readers. Also, it hides the incremental steps of going from the KG equation to Dirac's. In keeping the longer version, I was erring on the side of less obfuscation, not more.-Dilaton (talk) 21:03, 25 February 2012 (UTC)
 * No you're not. Removing "redundancy" is obfuscation. There's more than one road to comprehension. -- cheers, Michael C. Price talk 21:29, 25 February 2012 (UTC)
 * It might be worked back in, I was just trying to cut redundancy to make the article less of a mishmash. There's still a lot of redundancy though, such as with the connection to Pauli's theory.-Dilaton (talk) 22:02, 25 February 2012 (UTC)


 * I'll repeat: cutting "redundancy" does not aid comprehension. Stating a result in two different ways is benefical. -- cheers, Michael C. Price talk 22:07, 25 February 2012 (UTC)

Because I don't want an argument to occur and agree with both of you to different extents - right now I'll have a go at restoring the section. Please don't edit for a short while. Thanks -- F = q(E + v × B) 22:18, 25 February 2012 (UTC)


 * It was fairly quick, but see the section Covariant form and relativistic invariance. You'll notice I didn't blend into the sqrt of the KG eqn since I didn't think my own initial proposal through - its better suited to the section just mentioned. I also found a better reference that treats the issue more closely to what has been written in the subsection of the article. Please inform thoughts. Thanks, though I have a niggling feeling this is not what people would like... =| -- F = q(E + v × B) 22:31, 25 February 2012 (UTC)
 * Just a quick thought: did you mean "and there are solutions to the Dirac equation that the Klein–Gordon equation, in general, does not have." or do you mean it the other way around? As it currently stands it seems to contradict the statement a paragraph or two above it in the article. -- cheers, Michael C. Price talk 23:02, 25 February 2012 (UTC)
 * I meant exactly as it was first stated: "solutions to the Dirac equation solve the Klein–Gordon equation, not vice versa", but then I just deleted the end sentences since there is no point in having them. -- F = q(E + v × B) 23:12, 25 February 2012 (UTC)
 * okay. -- cheers, Michael C. Price talk 23:34, 25 February 2012 (UTC)

Pauli equation
Anyone up for moving much of the content in the section Comparison with the Pauli theory to the Pauli equation article? There seems to be significant overlap, so would reduce redundancy and the amount of maths visable to the reader on this article. -- F = q(E + v × B) 09:24, 26 February 2012 (UTC)
 * IMHO Dirac equation is off-topical almost at all, and if we had an article about electron spin, then these physical reasonings would rightfully belong to it. The only really important thing about equations (not field theory) is even not expressed, that Dirac equation is Lorentz invariant (and is based on the Dirac spinor representation) unlike Pauli equation which is Galilean invariant. Incnis Mrsi (talk) 10:18, 26 February 2012 (UTC)
 * Fair eneogh, thats one helpful opinion. Anyone else? -- F = q(E + v × B) 11:48, 26 February 2012 (UTC)
 * I agree that much of the Pauli theory material seems out of place here.-Dilaton (talk) 01:43, 4 March 2012 (UTC)
 * Sorry - hadn't come around to responding in all this time. For now, let’s just move the subsection to the electron spin article and rename it "Electron spin in the Dirac and Pauli theories". By all means change/revert if you disagree. F = q(E+v×B) ⇄ ∑ici 10:19, 26 April 2012 (UTC)

Reference suggestion
B Hatfield, Quantum Field Theory of Point Particles and Strings, Addison-Wesley, Reading, MA, 1989. — Preceding unsigned comment added by HCPotter (talk • contribs) 09:27, 4 March 2012 (UTC)

Pair production
In hind sight, the Dirac equation can be looked upon as extending the homogeneous photon energy-momentum relation [Potter] to regimes where it is nonhomogeneous; but, since photons appear to pair produce all known leptons [Akers] there may be at least three photon types: those that end as kinetic electrons, those that end as kinetic muons and those that end as kinetic tauons.

H. C. Potter, "Metanalysis validates comprehensive two part photon", Apeiron 18:3(2011)254-69. []

R. Akers et al., "A study of muon pair production and evidence for tau pair production in photon-photon collisions at LEP", Z. Phys. C60(1993)593-600.[] (HCPotter (talk) 08:10, 11 March 2012 (UTC))


 * We aren't going to be sticking in undue and self published material. You also have a conflict of interest, I suggest you stop with your text insertions. IRWolfie- (talk) 09:20, 3 April 2012 (UTC)


 * I removed the nonsense this user added to the introductory paragraph. Jpowell (talk) 11:45, 11 April 2012 (UTC)


 * See also Wikipedia talk:WikiProject Physics. I had a little chat with HCPotter on his user talk page, but I had to stop because I really have no idea what he meant with his most recent comment. Perhaps you understand? - DVdm (talk) 14:41, 11 April 2012 (UTC)

Identification of Observables
The section "Identification of Observables" begins with an equation without saying where it comes from. Best I can tell, it's based on the Dirac equation as presented in the article, but with some kind of electromagnetic potential term added. For a horribly stupid person such as myself struggling to understand this, it would be very nice if someone could add an explicit explanation of where precisely these q's and A's came from so I don't have to guess (and probably get it wrong). 66.68.80.131 (talk) 18:38, 28 May 2012 (UTC)


 * First things first - you are not stupid, because you already have some idea and its not an obvious subject (I don't know it all yet). =) The Ak and A0 (also denoted φ) are the electromagnetic potentials: Ak is the magnetic potential related to the momentum p of the particle (see kinetic momentum), and A0 is the electric potential related to the potential energy of the particle, the hamiltonian is the total energy (kinetic + potential, including the rest energy mc2, see Hamiltonian (quantum mechanics)). The index notation is used becuase A0 and Ak are both part of the 4-potential, and the components of 4-vectors are used seperatley. I will tweak the section and add those links where this is explained in more detial. =) F = q(E+v×B) ⇄ ∑ici 21:31, 28 May 2012 (UTC)

Discrepancy Betweeen Electron Hole Article and Dirac Equation Article
From http://en.wikipedia.org/wiki/Electron_hole "The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter, whereas the hole is just a fiction, used for modeling convenience."

From http://en.wikipedia.org/wiki/Dirac_equation#Hole_theory "In certain applications of condensed matter physics, however, the underlying concepts of "hole theory" are valid. The sea of conduction electrons in an electrical conductor, called a Fermi sea, contains electrons with energies up to the chemical potential of the system. An unfilled state in the Fermi sea behaves like a positively-charged electron, though it is referred to as a "hole" rather than a "positron". The negative charge of the Fermi sea is balanced by the positively-charged ionic lattice of the material."

I am not an expert on the subject but I would like to see this resolved! — Preceding unsigned comment added by Dudekahedron (talk • contribs) 15:04, 12 August 2012 (UTC)


 * An electron-hole in the Fermi sea is not the same as an electron-hole (= positron) in the Dirac sea. They have different masses for example. Whether one considers the electrons to be real or the holes to be real depends on what one considers the background state to be (the context: vacuum or a crystal). JRSpriggs (talk) 19:01, 12 August 2012 (UTC)

Mangled, Awful, Horrible
I see my work on this article has further deteriorated, with all manner of bad prose and worse physics (e.g. see above about "two kinds of Dirac field", which is pure nonsense). There is simply no way to make this article correct, and given how fundamental the Dirac theory is to all of particle physics, it should be a cornerstone of the entire Wikipedia physics effort. But it cannot be, because people without experience (students) keep adding irrelevancies and personal interpretations, and do so with no command of the English language.

If the editors of Wikipedia wish to give me full control of this article, I would be more than willing to put it into A-class form. As it stands, it is a sad commentary on the weakness of the Wiki idea - namely, persons of doubtful authority, and an excess of enthusiasm that substitutes for knowledge, target these fundamental subjects and make them their own personal soapboxes.

It is a terrible shame that something as important as the Dirac equation, both as a practical and an historical matter, is so poorly served by the Wikipedia. I would ask again that the editors of this project grant me autonomy to make this article correct. Correct in this case means - true to history, factually correct, written in a lean prose style that would not embarrass Dirac himself, conforming to standard textbook treatments of the equation and its consequences. I will not proceed until I can be sure that the work will not be vandalized by green students who lack both experience and depth understanding! Antimatter33 (talk) 09:41, 25 August 2012 (UTC)


 * Do not expect Wikipedia to make an exception to their general policy that all articles are open to editing by (virtually) anyone. I notice that you have provided no evidence that your qualifications to edit this article are greater than those of any other editor. JRSpriggs (talk) 16:59, 26 August 2012 (UTC)


 * Antimatter33: You might say I'm also responsible for DESTROYING IT. Just so you know and are happy I have no intension to touch this article, independent of your above comment... Support for that: Talk:Dirac equation/Archive 1, detraction: WP:OWN. Apologies. Maschen (talk) 07:50, 12 September 2012 (UTC)

On second thought, I will revert back to the revision by user:Antimatter33 on 13:37, 13 February 2011 yet still reinstate very minor tweaks in clean up, links, equation boxes, also the section: Dirac equation in curved spacetime. The restructuring of the article was largely by now blocked/left user:F=q(E+v^B). Hope everyone is happy. Maschen (talk) 21:46, 13 September 2012 (UTC)

Opening statement
"In quantum field theory..."

There was no quantum field theory when the Dirac equation was formulated. Do I need to say more? 76.105.101.35 (talk) 00:16, 14 September 2012 (UTC)

The Dirac equation is equivalent to a 4-th order PDE for just one component
Last year, I added a paragraph on the equivalency of the Dirac equation to a fourth order partial differential equation for just one complex or real component (and before that, I offered this amendment in the Talk, and waited for a month to make sure there were no objections). The paragraph was based on my article in the Journal of Mathematical Physics and has a reference to the article. Last month, the paragraph disappeared without any objections specific to the paragraph during a major re-editing. I tried to return the paragraph, but user Maschen undid my revision with the following comment: "adds nothing to understanding, text is nearly word for word from abstract of cited paper, signature of editor is inserted when it should not be)". I don't know about "adding to understanding", but the paragraph certainly adds new and fundamental knowledge, and I guess knowledge is at least as important for Wikipedia as understanding. If the wording of the paragraph does not look good, why not offer a different wording? Although it is not obvious that the text being close to an abstract of a properly published article is necessarily bad. I accept the following criticism though (and apologize for this mistake caused by inexperience with Wikipedia): "signature of editor is inserted when it should not be", so I added the paragraph without the signature today.

I think the main question is whether this paragraph is important enough to include it in the article. I am certainly biased, but I do think it is indeed important. The title of the article is "Dirac equation", and if the Dirac equation can be rewritten as an equation for just one (real or complex) component, how can it be unimportant? Furthermore, this is a new and nontrivial result.

Of course, I may be mistaken, so I would like to hear opinions of other people on this issue. Akhmeteli (talk) 15:23, 7 October 2012 (UTC)


 * I apologize for any offence, the revert was intended to be in good-faith. It's true that you proposed this last year (now archived) and no-one seems to have objected, although no-one ever signs their name in an article - that should be clear (but it's not a problem!).
 * By "adds nothing to understanding", I wasn't sure what most readers could get from the paragraph; what the equation is about and its significance in particle physics (then arguably all the stuff on spinors is technically necessary and not so penetrable either...).


 * On a general note: Given the edit history of this article over the last year or so, I will not touch it (and thereby interfere) again (except for true vandalism reversion). If others (like Antimatter33 above) complain later the article has been vandalized it's on others to fix. Maschen (talk) 18:42, 7 October 2012 (UTC)


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


 * I'm not an expert in this particular field, so I can't say much on if this paragraph should be included or not, but here are some general remarks: First, it's very good that you brought this up on the talk page first last year and now again, it's a pity that nobody replied the first time.
 * Second, that the wording is very close to the abstract of a published paper is indeed a problem. Not because we don't like it, but because it might be a violation of copyright laws. Even though you wrote that text yourself, the copyright is most likely owned by the publisher, and they probably didn't license it in a way that's compatible with use on Wikipedia. The easiest way to solve this is usually to rephrase the paragraph, and I guess you're most qualified to do that without introducing errors.
 * Third, is the paragraph worth including at all: As far as I can see your article has been cited only once yet, and that in a book written by yourself. This is not necessarily a problem, since we're only talking about a small addition to an existing page. But of course not every paper written in that field can have it's own paragraph here. So it will be good to get some opinions whether this one is noteworthy. &mdash;&thinsp; H HHIPPO  19:50, 7 October 2012 (UTC)
 * I agree that generally copyright is an important consideration, but I don't think there is any copyright problem in this particular case. First, the text in the suggested paragraph differs significantly from the text in the JMP article abstract, second, the journal does allow this kind of reuse: "Permission for Other Use/Permission is granted to quote from the journal with the customary acknowledgment of the source. Republication of an article or portions thereof (e.g., extensive excerpts, figures, tables, etc.) in original form or in translation, as well as other types of reuse (e.g., in course packs) require formal permission from AIP and may be subject to fees." (http://jmp.aip.org/about/rights_and_permissions). The two phrases (significantly modified) cannot be considered "extensive excerpts".Akhmeteli (talk) 21:13, 7 October 2012 (UTC)
 * There are also the issues of WP:verifiability and WP:notability, which might suggest that regardless of its importance, it is essentially indistinguishable under these criteria from many other citations that would be excluded from Wikipedia. This is a primary source, apparently cited only by the author, and being edited into WP by the author. WP is not where new results are published; it merely summarises the established knowledge: it is a tertiary sourse. I suggest you review these policies/guidelines carefully yourself (there are also some relevant essays on how and why these arose, which you might find in the process). While the result is interesting and relevant, my first-pass perception is that it is not yet notable. As a side-comment, your choice to include it in the section Comparison with the Pauli theory seems to me to be entirely inappropriate. — Quondum 05:14, 8 October 2012 (UTC)
 * I am not sure there are any problems of verifiability. Wikipedia requires a reliable source and explains that "Where available, academic and peer-reviewed publications are usually the most reliable sources, such as in history, medicine, and science." (http://en.wikipedia.org/wiki/Wikipedia:Verifiability). The paragraph in question has a reference to a peer-reviewed publication in a reputable journal, so the condition of verifiability is satisfied, as far as I can judge. The result is new in the sense that it is quite recent, but it is not new in the sense that it has been already published elsewhere, so it is not "original research" from the point of view of Wikipedia.
 * As for notability, on the one hand, your reference to the Wikipedia guidance on notability is not quite relevant as they write there: "The notability guideline does not determine the content of articles, but only whether the topic should have its own article.", on the other hand, I agree that any material in Wikipedia articles should be significant enough. Of course, I am not the best judge of importance of this result, but when I wrote in the journal article that the result belongs in textbooks, neither the referees (there were two of them), nor the editors raised any objections. Whether the result belongs in Wikipedia... we'll see what the community thinks about that, but I am grateful to you for kindly calling the result "interesting and relevant".
 * I agree with you that the paragraph does not look good in the section Comparison with the Pauli theory, but I was not able to find a better place: I thought that the paragraph should not appear before the Dirac equation in electromagnetic field is written out, and it is in this section that this happens for the first time. But neither the subsequent sections look as a good place for the paragraph. Any suggestions?
 * Akhmeteli (talk) 05:25, 9 October 2012 (UTC)
 * I can't argue with the distinction between notability for an article and for something in an article. One has to be cautious about inclusions of this nature; some people get pretty heated about something they feel should be in, but turns out to be crackpot. It is a little unfortunate that your result has apparently not been taken further; it would, for example, have been interesting to have a differential equation for a real scalar field (in the sense of a type (0,0) tensor) that then determines every component of the spinor field.
 * As to a suggestion, perhaps you should precede the paragraph with its own subheading at the same level as the previous one. You may get a negative reaction from some; but hopefully some editors with greater knowledge in the field than mine could do something constructive with it. The lack of much response so far suggests that most editors may be a little unsure of how to deal with it.
 * Incidentally, my own encouraging remark must be considered from whence it came: a dabbler in the area. To me, it is not clear that it is not an obvious consequence of the nature of the equation. AFAICT, getting to a single 4th-order PDE in one complex component should be a universal result in any 1st order PDE in a complex vector of four components. That this component can be transformed into a real component is less obvious. OTOH, doesn't the Klein–Gordon equation provide a 2nd-order PDE for each separate complex component? Wouldn't the same gauge transformation trick work here, or alternately a separation of the real and imaginary parts directly result in a 4th-order PDE in one of the parts? This is perhaps not the place to discuss this, but it does suggest that the result is not ideal for presenting as is without some further development of the point. — Quondum 19:46, 9 October 2012 (UTC)
 * Thank you for your comments. As for further development...The result does provide a PDE for just one component, and all the other components can be expressed via the first component, but this component's transformation properties under the Lorentz group are not those of a scalar - the component transforms together with its derivatives.
 * Your suggestion on a subheading is reasonable, but, as you say yourself, one cannot be sure that will be well received, so maybe I should wait and see...
 * No, for an arbitrary system of four first-order PDEs for four components, you cannot get an equivalent fourth-order PDE (see, e.g., Commun. Math. Phys. 269, 545–556 (2007)), so the result is nontrivial (the inverse is true though: for a PDE of an arbitrary order for one function, you can build an equivalent system of first-order PDEs for several functions.) The Klein-Gordon does provide a second-order PDE for each component, but only if electromagnetic field vanishes or in some other special cases, whereas my result generally holds for arbitrary electromagnetic field. On the other hand, as Schroedinger showed, the gauge transform trick does succeed for the Klein-Gordon equation for arbitrary electromagnetic field, providing an equivalent equation for a real, rather than complex, function, but that does not affect the value of my result for the more realistic Dirac equation.
 * Akhmeteli (talk) 02:51, 10 October 2012 (UTC)
 * Okay, good to have my half-baked conjectures out of the way and your result therefore being of greater significance as you suggest. You misinterpret me on the subheading: I was not saying you'd get objections to insertion of a heading; it would suitably highlight and separate the addition to allow others to focus on it more easily. The objections/modifications would be to the detail; I for one feel that it is a bit sketchy. You would be a better person to choose one, perhaps along the lines of the heading for this thread.
 * On a side-track, it's pretty obvious one of four components could not be a Lorentz invariant on its own. I was thinking along the lines of the electromagnetic vector potential, where an order-1 tensor A defines an order-2 tensor F. — Quondum 06:40, 10 October 2012 (UTC)
 * OK, thank you for the suggestion. I could insert, e.g., the following subheading: "Equivalency to a fourth-order equation for one component".
 * As for sketchy details, again, this hinges on the community's opinion on the importance of the result (I guess there is no doubt about relevancy), and I am not the best judge of that. I would be happy to add details, e.g., write out the 4-th order equation, but I guess I should wait with that. I think those interested in details can look at my journal article. By the way, somebody has deleted the link to the article on my web-site (the journal allows me to display the article at my web-site). I am going to restore this link as elsewhere the article is behind the paywall. I am going to make these amendments (subheading and link) in a week, if there are no objections.
 * Thank you for the explanation of your words: "it would, for example, have been interesting to have a differential equation for a real scalar field". I know that something should be done in this direction, furthermore, I specifically wrote in the article: "Presenting the above results in a more symmetric form is beyond the scope of this work.", but I have to choose my battles: I have too many projects on my hands, and I have been especially busy with a different one (arXiv:1208.0066) over the last year.
 * Akhmeteli (talk) 09:43, 11 October 2012 (UTC)
 * I've reinserted the (probably unitentionally) removed public reference and inserted a heading (hopefully less of a mouthful, but maybe still not ideal) to facilitate comment from other editors. Perhaps we can wait for comment from others at this point. — Quondum 18:15, 11 October 2012 (UTC)
 * Thank you very much indeed!Akhmeteli (talk) 11:55, 12 October 2012 (UTC)