User talk:YohanN7/Archive 1

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TI

Do you still find Transfinite_induction#Relationship_to_the_axiom_of_choice misleading after the revisions I made? An outside opinion like yours can be useful in finding hidden gaps in exposition. I can make another attempt if this one didn't succeed. — Carl (CBM · talk) 13:48, 22 July 2009 (UTC)

Talk: Special unitary group #Physics vs mathematics convention

[1] "exponental", "scentences", "paricular". Incnis Mrsi (talk) 08:22, 23 September 2012 (UTC)

Oops, missed "scentences". The other two I blame on my keybrd. It tens to miss strokes. YohanN7 (talk) 11:10, 23 September 2012 (UTC)

Quick note about the representation draft

There's line about so(3;1) being simple, followed by "That is, so(3;1) can not be decomposed into a direct sum of simple pieces." I'm not sure my intuition about semisimple algebras applies here, but I don't think that's a correct characterization of simplicity. For rings, a simple ring R is characterized by having no nontrivial homomorphic images. However a simple ring, (and I believe a simple Lie algebra) can still be semisimple, whence it decomposes into simple pieces. Rschwieb (talk) 21:36, 30 September 2012 (UTC)

All simple Lie algebras are semisimple by convention. One-dimensional algebras are not simple (by convention again). What is meant in the draft is that so(3;1) is semisimple and simple. [This is the key to so(3;1) having no unitary finite-dimensional irreps.] I'll try to improve on claroty in that section.

The characterization of simplicity is probably the quirk here. The statement is likely to be correct (I have no proof myself, but there are mentions of this (without proof) in reliable sources.) A correct statement would probably be "There is no real linear Lie algebra isomorphism h:so(3;1)->g₁⊕g₂...g_n where n>1 and the g_i are all nontrivial.

There is a separate talk page for the draft here: User talk:YohanN7/Representation theory of the Lorentz group. I have copied this section there. YohanN7 (talk) 10:41, 1 October 2012 (UTC)

Group representations of the BW equations

Hi YohanN7. It's nice to see a third person (me not included) with some interest in the BW equations... Crowsnest fixed my reference errors and complimented nicely (even though the article is still useless as it stands...), also Quondum fixed more of my erronous formatting...

I noticed from here and here that you have seen the article, and that it needs background on group representations found in the literature, and agree. I'd add this myself, but it's frustratingly confusing... If you understand them and have time/are able to - feel free to add this content to the article. There are plenty of papers which source such representations (and I can find more if needed). Many thanks for any help, M∧Ŝc²ħεИ_τlk 17:36, 18 December 2012 (UTC)

Hi!

I'd be happy if I could contribute. Regarding the BW equations, my hunch is that a derivation from the point of (a particular) group representation would pretty much parallel the corresponding derivation of the Dirac equation. I attempted to incorporate the latter ([[2]]), in the context of general finite dimensional representations of the Lorentz group.

I don't see how to make such a derivation, at the same time, shorter and more comprehensible. Math people have tended to say I manage to state the obvious in an obscure way using 20 pages, and physics people generally don't like the approach, since it isn't the way the DE was originally though of. I am a little bit put off by this, not because they are wrong, but because I can't see that I have time and the knowledge to be able to contribute in a way that is more than 10% likely of not being permanently reverted.

Also, if there is a place for reasoning of this sort (SR + QM + Representation Theory -> Free Field Equations of Quantum Fields) in Wikipedia, then is is probably best to place it in a separate article. I could see the latter half (Consequences of Lorentz Invariance) of my proposed article (or anybody else's) being such a place. At present (at least the last time I read the more general QFT articles) that approach isn't used (Lagrangian formalism, canonical quantization, and/or path integrals are preferred as foundations). It is a very long way to go.

I should also point out that I have not yet read the present article carefully. Keep in mind too that I am a layman. YohanN7 (talk) 13:08, 19 December 2012 (UTC)

That's very reasonable of you. The Lorentz group was the original approach of Bargmann and Wigner [3] (there was a long history section which slightly indicated BW's group-theoretic approach, but went off a tangent about relativistic wave equations in general...). Your article looks extremely impressive! Although it would be overkill for the BW eqns (and as you point out, too technical).

About half of the content of the article is essentially the Dirac equation, although necessary to set the scene, so paralleling representations with the Dirac formalism is fine.

What I mean to insert a very brief outline (rather than a derivation) of what all these group representations mean in the context of the BW formalism (although it may be harder than just anticipated - there appear to be numerous formalisms: Galilean-relativisitic formaultion, the so-called "2(s + 1) theory" and Joos-Weinberg equations [4], the Bhabha equations are closely related [5], a general formalism on relativistic Hamiltonians for particles of any spin [6], and probably more... so we need to take that into account).

Anyway thanks again! M∧Ŝc²ħεИ_τlk 13:46, 19 December 2012 (UTC)

Now I have a lot of reading to do. This is something I look forward to. When you mention "2(s + 1) theory", do you think that Landau & Lifshitz "Quantum Mechanics" is a good starting point? As I recall, their approach to spinors was, at the outset, a "2(s + 1)" approach, if I guess correctly about the meaning of the term. Also, it is listed as a reference in [7], as well as in Weinberg's "The Quantum theory of Fields vol 1". (Besides, I have it somewhere!) In terms of representation theory one would pass from an "(m,n)-theory" (two indices) to an equivalent theory with more indices, but taking on only two values? YohanN7 (talk) 13:18, 20 December 2012 (UTC)

From the article: "Unlike the Dirac equation, the BW formalism comprises intrinsic contradictions and difficulties when the electromagnetic field interaction is incorperated". This needs some qualification. For one thing, massive particles with high spin surely exist, take, for instance, various stable charged nuclei. These may not be elementary, but the problems can only exist for point particles.

I'll quote what Weinberg writes (QFT vol 1 section 5.7): Inconsistencies, non-causality, unphysical mass states, and non-unitarity are not inherent in the theory of high spin fields (field equations), due to the way they are constructed. 1.) Problems with higher spin are reported in QFT only "when one goes beyond perturbation theory". These problems have all been found in the presence of a C-number external field (which is sort of a semi-classical approximation). 2.) Even for C-number external fields, all problems have been found for very simple couplings. They may disappear as more complicated terms are included. It is expected that higher spin fields, if they exist, have all possible interactions allowed by symmetry principles. 3.) There is some ambiguity about the term "simplicity of interaction"; In the "interaction picture", free fields can be written in several ways, so that "simplicity of interaction" alone doesn't mean much. 4.) String theory provides examples of massive spin 2 fields.

These quotes are, of course, not full quotes, and I hope I haven't written anything too wrong. YohanN7 (talk) 15:31, 20 December 2012 (UTC)

Landau and Lifshitz are reputable and reliable sources, so they would make a valuable addition to the literature list (should be mentioned in E.A. Jeffery's paper somewhere). Note that "2(s + 1)" is an incomplete typo - it should be "2(2s + 1)"... Sorry!

As for the citation on the EM interaction contradiction, that paper [8] doesn't appear to be a professional article written in a peer-reviewed journal, just a paper written by someone at a university in Turkey that made its way onto arxiv.org ... It makes a good further read, but all I had at the time. I agree it needs qualification, and it will be replaced soon. There are apparently problems with the relativistic wave equations when the EM field is introduced: you can't use the "minimal EM field coupling prescription" as with the Dirac equation, i.e. make the change P_μ → (P_μ − eA_μ) (?)... For example [9] (in article) and [10] (not in article). These sources seem to agree with what you're saying, but I'll have to look into C-number external fields in more detail... The closely related Bhaba(-Lubanski) formalism apparently arose from higher-spin fields and symmetric components, when incorporating interactions same IoP link above.

Basically everywhere, more qualification and depth like this is needed...

P.S. Just to be sure; you do have access to papers like at sciencedirect.com and IoP? Some sites only allow members or subscribers... (I have access via the uni library...) If not I can email the pdf's. Thanks, M∧Ŝc²ħεИ_τlk 19:22, 20 December 2012 (UTC)

I don't have institutional access (being an amateur) to archives and journals. Sometimes links work, but usually they don't. Links 8 and 10 above do work, the others don't. (Truly pivotal publications are usually possible to dig up somehow.)

I don't know about the details of the problems with higher spin with interactions, I'm not sure I'd even understand [11], the abstract indicates that a higher level of mathematical sophistication than I have is required (which doesn't stop me from trying). Nor does my main QFT reference (Weinberg) go into the technical details because of the above listed objections he has, in the context (chapter 5) of where the general results for quantum fields (arbitrary spin, or rather arbitrary representations of the Lorentz group) are derived. But High spin, on the other hand, makes a theory less likely to be renormalizable. The real question may be what status to give the renormalizability requirement. Quantum Gravity (of which I know absolutely nothing except that the graviton is a massless spin 2 particle) is said to be non-renormalizable, whatever it really is. YohanN7 (talk) 14:44, 21 December 2012 (UTC)

Good points; normalizability is not even mentioned in the article, though the papers don't seem to make it clear cut (I may have overlooked). This is a problem; not every paper says everything, and those which mention particular points may not be very clear because they assume background knowledge of practitioners...

I don't have Weinberg's book right now, though it would be valuable to include Weinberg as a reference also (at the very least, as a "further reading"). Feel free to add to the references section, if you want to. M∧Ŝc²ħεИ_τlk 16:38, 21 December 2012 (UTC)

I have added Weinberg to the references. I think it is quite appropriate because Weinberg's adopted approach to what a "particle" is is that of Wigner. Regarding the connection between different approaches (different forms of the BW equations), this can perhaps be approached purely mathematically in a short section. For instance, one should be able to represent a spin N/2 object by considering N spin 1/2 objects (tensor product), and by extracting an appropriate subspace ("parallel" spins as to "add up" constructively to N/2 in a physical picture, the SL(2,C) (or SU(2)) subrepresentations being present in just about every classical group representation mathematically). Now I managed to sound really obscure. I'd better have a look in the math literature. YohanN7 (talk) 22:48, 21 December 2012 (UTC)

Not obscure at all, agreed that a separate section would be better, only recently the group representations have been included next to the equations for completeness. Let's at least start this section today.

I've had some exposure to SU(N), U(N), SO(N), O(N) groups, although need to familiarize with SL(2, C), since this is the required group.

Also thank you for adding Weinberg! M∧Ŝc²ħεИ_τlk 09:30, 22 December 2012 (UTC)

The relationship between SU(2) and SL (2,C) is fortunately quite simple. The group SL (2,C) is the complexification of the group SU(2) (best expressed in terms of Lie Algebras). In the other direction, SU(2) can be said of being a (compact) real form" of SL (2,C). The usefuleness of SL sl (2,C) is that it is a subgroup subalgebra of most (all?) classical groups algebras, including the Lorentz group algebra. SL (2,C) is also the unique universal cover of the Lorentz group, meaning the unique simply connected covering group of it. YohanN7 (talk) 13:28, 22 December 2012 (UTC)

Ok, thank you for that. For now I'm going to break away from the article, since I seem to only be making many little edits each day, and the article isn't improving much, although will return to it later after much more (needed) thorough reading (by all means we can keep the discussion running)... M∧Ŝc²ħεИ_τlk 17:35, 22 December 2012 (UTC)

I found a paper which may be useful on interactions for massive particles with arbitrary half-integer spin (it's freely avalaible):

J. Niederle, A. G. Nikitin (2004). "Relativistic wave equations for Interacting, massive particles with Arbitrary half-integer spins" (PDF). Kiev (Ukraine), Prague (Czech Republic). arXiv:hep-th/0412213.

Seems to have content relevant to the article... M∧Ŝc²ħεИ_τlk 20:09, 22 December 2012 (UTC)

I am at this point struggling to get a better detailed understanding of Clifford algebras. I know how to squeeze out 4- and 6-dimensional spin representations from them (by this I essentially mean extracting an appropriate subspace from tensor products of C⁴ equipped with a Lorentz metric and a product operation (matrix multiplication in practice, given a basis)), but I don't know the exact procedure in the general case, at least not well enough to try to describe it to others.

Thanks for the reference. It seems very readable and relevant. In my article, I got to as far as "half" of the Rarita-Schwinger equations (isolating the spin 3/2 subspaces), the rest were lose threads. If i manage to knit those lose threads together, then perhaps something short and comprehensible can be extracted. YohanN7 (talk) 14:50, 4 January 2013 (UTC)

Hi, sorry I’ve been separated from this for a while, busy with work (aren’t we all, though...). Replied to your post just now. Thanks, M∧Ŝc²ħεИ_τlk 20:17, 11 February 2013 (UTC)

Timestamps of talk posts

Do not do [12][13]. If you add a new chunk of text, then you must mark it with the current date, not to insert it between an actual post of 23:00 and the signature with the 23:00 timestamp. Incnis Mrsi (talk) 07:43, 18 February 2013 (UTC)

Well, other than that, what do you think about throwing in a derivation outline of that spin transformation (S in the bispinor article) either there or in Representation theory of the Lorentz group? YohanN7 (talk) 08:03, 18 February 2013 (UTC)

WP articles Quantum field theory and Relativistic quantum mechanics

are the same link (you may already know). For RQM would it make sense to replace the redirect for an article? Thanks, M∧Ŝc²ħεИ_τlk 10:21, 7 April 2013 (UTC)

Oh, yes. No RQM article is a pretty huge omission. YohanN7 (talk) 11:02, 7 April 2013 (UTC)

You'll find an infinite number of ways relativistic quantum mechanics can be improved, by all means do so. (I plan to add more scope and references later by the way). Thanks in advance, M∧Ŝc²ħεИ_τlk 11:05, 12 April 2013 (UTC)

P.S. I copied the first part of this section you wrote into the RQM article. Hope you don't mind. M∧Ŝc²ħεИ_τlk 08:25, 14 April 2013 (UTC)

Interaction about KG – let's put it to bed

Hi YohanN7, I apologize for getting under your skin like this. I don't think that it will serve any purpose to try and analyze who did what; I regret having made comments that do not belong at Talk:Gamma matrices in the first place and we do not seem to be achieving anything by pursuing it. We seem generally to somehow trigger a reaction in each other with trivia. I enjoyed our interaction about representations of Clifford algebras and was somewhat heartened that it did not derail, and that we managed to navigate to a decent conclusion; in the process I also learned something about the subject matter. I tend to make comments based on my (uneducated) perception of plausibility while at the same time being very picky about details. I really hope we learn to interact in a way that doesn't involve quite so much unimportant detail and does not devolve into simply steering clear of each other for fear of triggering similar energy-consuming interactions. —Quondum 01:01, 13 November 2013 (UTC)

No problem. I didn't see this until now.

On the issue, there is in fact a little something about this in Relativistic wave equations. As far as "plausibility" goes, the solutions of an RWE must transform under some representation of the Lorentz group. This actually fixes the space of solutions of the RWE, given a representation, so that is not that surprising that the equation as well can be deduced. We have been talking about the free field equations (no interactions) for massive particles. But it should be no surprise that the interaction terms as well are constrained by spacetime symmetry. For a derivation of the Dirac equation, see here: User:YohanN7/Representation_theory_of_the_Lorentz_group#Free_field_equations_and_gauge_principles. It is also true that the free field equations for massless particles follow from Lorentz invariance, but in this case, the KG equation isn't satisfied. For instance, the free field Maxwell equations follow from Lorentz symmetry. YohanN7 (talk) 21:44, 1 December 2013 (UTC)

Given that the rest mass of a photon is zero, I have difficulty distinguishing the KG equation from the free-space electromagnetic wave equation. But no matter. —Quondum 00:35, 2 December 2013 (UTC)

Not sure what you mean, but yeah, putting m = 0 in the KG equation turns it into the same form as the free Maxwell equation. The important thing though is that you don't believe that I'm making all this up. Why would I do such a thing? A formal proof of what I say is too complicated to give here. You have to go to the references. Weinbergs QFT volume 1, chapter 5 is the best ref I know of for this. YohanN7 (talk) 01:10, 2 December 2013 (UTC)

At the level of informality that I'm working at this is hardly critical. But I do not disbelieve you – I'm simply slowly trying to put together little snippets of understanding. I still have a long way to go before I can make the start of a general statement in representation theory, and I have not yet come to grips with spinors, or for that matter, spin. So don't be surprised if you see uninformed "it looks like" statements coming from me. Right now, I'm focussing on abstract geometries, not something I'd have thought would interest me.  ;-) —Quondum 04:59, 2 December 2013 (UTC)

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MatthewVanitas (talk) 06:31, 19 December 2013 (UTC)

thank-you

thank you for laugh on pluralization. feel free to delete this. Lfahlberg (talk) 16:15, 5 January 2014 (UTC)

Italic symbols

Your edit is fair (I like the use of {{math}}), but it is a standard WP guideline to retain the italics. A global replacement nowrap→math would probably have done it, plus what you added. Note also that {{math}} incorporates the {{nowrap}} functionality, so nesting a nowrap template around a math template serves no purpose. —Quondum 06:49, 23 January 2014 (UTC)

Too bad, I'll miss the nesting... (not). I actually thought for a while {{math}} defaulted to italics. It doesn't apparently. Nor can it handle equality signs (which shouldn't come as the most unexpected sign in a mathematical expression (I know, the 1= trick, very obvious and natural). The situation with math formatting is a bit pathetic. YohanN7 (talk) 08:06, 23 January 2014 (UTC)

Yeah. The {{tl:var}} template applies italics too, e.g. x, which may be what you were thinking of. Agreed about math formatting – MathJax is unusable because it is so slow, PNG has sizing and kerning issues, and HTML is too limited. And so people argue about a bunch of bad options with no good choice. —Quondum 15:15, 23 January 2014 (UTC)

But note in Template:Math enclosing an = sign with double braces works nicely, and italicizing inside the math template produces accurate and elegant expressions.

So you can just take the italic expression and enclose it inside a math template, double bracing the =s. It's fussy, but there is no real problem. Cuzkatzimhut (talk) 19:03, 23 January 2014 (UTC)

Spacing binary operators default? x ⊕ y, yes, of course, but x⊗y feels more natural than x ⊗ y. Whether a binary operator is "additive" or "multiplicative" in nature makes the difference to me. Is there an official standard?

@Cuzkatzimhut There is no real problem of course, except that by tomorrow I have forgotten how to do it. Things of this nature simply don't stick. Then there is the vertical bar, really bizarre; |−4| = 4, which I yesterday would have written (after hours of researching) as |−4| = 4 (see source)! YohanN7 (talk) 22:07, 23 January 2014 (UTC)

I linked from my edit summary to the MOS where it talks about spacing binary operators – I think that's about as official as it gets. It seems to function as a distinction between unary and binary operators. I understand where you're coming from, since multiplicative operators binds more tightly than additive operators. (An aside: in GA, the ∧, ⋅ and similar operators are considered to bind more tightly than the geometric product which is denoted by juxtaposition, i.e. a ∧ bc = (a ∧ b)c, yet the spacing would suggest the opposite: a ∧ (bc)!) However there is actually a problem with spacing in that it cannot adequately reflect multiple levels of binding precedence. Distinguishing unary from binary + and − and making sense of a string of adjacent operators (all except zero or one being unary) seems to me the most obvious value of the notation, but in any event I prefer a uniform standard, whatever it is, and here it seems to be spaced binary operators. —Quondum 04:43, 24 January 2014 (UTC)

Dedekind-infinite set

Thank you for notifying me. I'm afraid I don't have much to add to the discussion at Talk:Dedekind-infinite set#The lead. Please feel free to fix any (of my many) mistakes you find. —Tobias Bergemann (talk) 08:08, 7 February 2014 (UTC)

@Tobias Bergemann I don't think you understand. What was discussed at Talk:Dedekind-infinite set#The lead between Trovatore and me regarded my poor terminology. It has nothing to do with my issue with the lead. The problem is that the claim comes without context as a standalone sentence in the lead. Fine in a set theory book (where a context is present), but not in an encyclopedia. YohanN7 (talk) 13:33, 7 February 2014 (UTC)

Yet one discussion

I’d appreciate your participation at talk: Euclidean space‎‎ #Velocities became hyperbolic?. I’m tired to explain obvious things. Incnis Mrsi (talk) 17:27, 16 February 2014 (UTC)

Hello! (Random question)

Hi YohanN7! A while ago you wrote this comment on the math project page:

But you are right about symmetric bilinear forms. They don't yield anything interesting (I think they are automatically degenerate, not sure, can check this out later) in the quaternionic case.

This intrigued me a little, but I had not been following the thread of the conversation, so I have to ask you here to explain what context you were thinking of.

In general, there are nondegenerate bilinear forms for all division rings and even for valuation rings which aren't necessarily fields, and as far as I know they are very interesting... Rschwieb (talk) 15:22, 20 March 2014 (UTC)

I checked this out in Lie Groups -An Introduction through Linear Groups by Wulf Rossman. Actually it says that there are no nonzero bilinear forms at all in the quaternionic case. YohanN7 (talk) 07:15, 22 March 2014 (UTC)

Sorry about the very brief comment, but I'm in kind of a hurry. This thing is a bit puzzling to me too. The explanation Rossmann is giving has bugs (there are millions of typos in that otherwise excellent book). YohanN7 (talk) 23:58, 22 March 2014 (UTC)

I'm butting in here, but if one is talking about bilinear forms on a vector space (a left D-module) over a (strictly noncommutative) division ring D, then it is probably important to define "bilinear form" more specifically. For example, if we define a form to be bilinear on left scalar multiplication, i.e. that B(λx,y) = λB(x,y) and B(x,λy) = λB(x,y) for all λ, x, y ∈ D, then I would not be surprised if no nonzero bilinear forms exist. Normal multiplication of quaternions does not satisfy this definition of a bilinear form. Useful bilinear forms on a bimodule might exist, though if the definition of bilinearity is changed to B(λx,y) = λB(x,y) and B(x,yλ) = B(x,y)λ for all λ, x, y ∈ D. Such a bilinear form may still necessarily be zero if required to be symmetric, though. —Quondum 17:20, 23 March 2014 (UTC)

Rossman uses

$\phi (x\alpha ,y\beta )=\alpha \phi (x,y)\beta ,$

and he gives reasons for it. His demonstration that no nonzero bilinear forms exist almost certainly has typos in it. But sesquilinear froms exist, satisfying

$\phi (x\alpha ,y\beta )=\alpha \phi (x,y){\bar {\beta }}.$

It is probably the case that neither symmetric nor skew-symmetric nonzero bilinear forms exist, and hence none at all, because they can always be split into a symmetric and an skew-symmetric part. It shouldn't be to tricky to prove this, but I'm really exhausted and feel downright stupid at the moment. :D YohanN7 (talk) 17:45, 23 March 2014 (UTC)

It's trivial to prove that either the division ring is commutative or the bilinear form is zero, except for the bimodule case that I mentioned. So I'm interested to see what @Rschwieb: had in mind. —Quondum 19:56, 23 March 2014 (UTC)

I hadn't thought about it deeply, and I just had the naive inner product in mind. I can see now that enforcing linearity becomes problematic. Using Rossman's setup: $\phi (x\alpha ,y\beta )=\alpha \phi (x,y)\beta ,$, you can just pick x,y to have inner product 1 (or any real number, for that matter) and then enforcing symmetry or skew-symmetry you get $\alpha \beta =\alpha (x,y)\beta =\phi (x\alpha ,y\beta )=\pm \phi (y\beta ,x\alpha )=\pm \beta \phi (y,x)\alpha =\pm \beta \alpha$. In either case, you don't get an identity that holds in the quaternions. If it were symmeric, this would prove the divison ring is commutative. If it is skew-symmetric, you just get the equation ab+ba=0 for all a,b... I don't immediately know if this would force commutativity again, but one gets the feeling that it probably has to be commutative.

The prototype for all these problems though is looking at the metric as a Gram matrix. A symmetric form would still have to have a symmetric matrix, and one can see how the noncommutative scalars interfere with swapping sides. It seems like this defeats the other (very natural) "bimodule" version of the form since there just seems to be no way to reconcile the side issues.

The sesquilinear form axioms miraculously solve this problem, though, due to their ability to reverse the twist that the side-swapping creates.

So I've convinced myself that symmetric and skew symmetric forms aren't feasible on spaces over division rings. Thanks for bringing this up. Rschwieb (talk) 17:47, 24 March 2014 (UTC)

I think you can simplify the argument in the skew-symmetric case. The equation ab+ba=0 implies that all element pairs anticommute (if that is the term for it). This is impossible since there are pairs of elements that actually commute, just take one of them as a "real" quaternion, a1 + 0i + 0j + 0k for a real and non-zero. YohanN7 (talk) 18:05, 24 March 2014 (UTC)

Hah, yes, I suppose that is the twin argument. There are elements that don't commute and there are elements that don't anticommute. Clearly one can judiciously always choose a pair of commuting elements in a division ring to make a contradiction. Rschwieb (talk) 23:03, 24 March 2014 (UTC)

It seems we are all roughly on the same page. I was thinking of the simpler proof along the lines of (working with a division ring, no need to consider symmetry or antisymmetry at all):

• Left-module case: $\alpha \beta \phi (x,y)=\alpha \phi (x,\beta y)=\phi (\alpha x,\beta y)=\beta \phi (\alpha x,y)=\beta \alpha \phi (x,y)\Rightarrow {\alpha \beta \equiv \beta \alpha \vee \phi (x,y)\equiv 0}.$
• Rossman case: $\alpha \beta \phi (x,y)=\phi (x\alpha \beta ,y)=\beta \phi (x\alpha ,y)=\beta \alpha \phi (\alpha x,y)\Rightarrow {\alpha \beta \equiv \beta \alpha \vee \phi (x,y)\equiv 0}.$
• Bimodule case: This does not suffer from this "must be zero" problem, as with the sequilinear case, but there will restrictions as I have already alluded to, as with the equivalent of Hermitian forms for sesquilinear forms.

Interesting, in all. —Quondum 23:34, 24 March 2014 (UTC)

It actually is Rossman's intended proof, modulo a big bug in his book, and modulo a smaller bug in your explanation.

• The real Rossman case: $\alpha \beta \phi (x,y)=\phi (x\alpha \beta ,y)=\beta \phi (x\alpha ,y)=\beta \alpha \phi (x,y)\Rightarrow {\alpha \beta \equiv \beta \alpha \vee \phi (x,y)\equiv 0}.$

My initial failure in seeing the light was that I somewhere wrote,

$\beta \phi (x\alpha ,y)=\alpha \beta \phi (x,y),$

which is a too gross, yet subtle, an error for me to discover once I'd have introduced it. :D:D:D YohanN7 (talk) 08:23, 25 March 2014 (UTC)

Oops, I see I have a copy-paste typo. Dropping the excess alpha makes it the same. This all leaves us with the interesting conclusion that bilinearity is in some sense intrinsically tied to commutativity of the underlying division ring. —Quondum 14:56, 25 March 2014 (UTC)

Since division rings are so closely tied to geometry, I was pretty surprised this happened. I guess this gives a huge boost to the motivation for sesquilinear forms, though. I'm very familiar with Clifford and Weyl algebras built with symmetric and antisymmetric forms, and now I'm really wishing I knew more about the sesquilinear version. I found this : http://www.ams.org/journals/tran/1969-138-00/S0002-9947-1969-0238876-0/S0002-9947-1969-0238876-0.pdf which suggests that even Jacobson had thought about them. Rschwieb (talk) 15:49, 25 March 2014 (UTC)

They also form, together with the bilinear forms, a unifying foundation for the Classical groups (which is otherwise a bewildering maze, at least when it comes to notation). I have long-term plans for a better treatment of them in that article (using Rossman as a ref). See that articles talk page. YohanN7 (talk) 16:55, 25 March 2014 (UTC)

@R: In geometry, the generalization of bilinear forms might have problems, but perhaps that problem does not apply to quadratic forms: $q(\alpha x)=\alpha ^{2}q(x)$? Also, sesquilinear forms on complex vector spaces do not deal with non-commutativity (IMO they are simply a shorthand way of realing with a class of real vector spaces), even if in quaternions it may have the right effect. I'm also not sure what you're referring to w.r.t. Clifford and Weyl algebras, as the bilinear forms are over a field AFAIK. Nevertheless, the geometric connection does suggest that exploration of quadratic/bilinear forms for this use should be interesting.

@Y: The connection with the classical groups is definitely interesting, and I see that they refer to modules rather than vector spaces there (including quadratic, sesquilinear and skew-symmetric forms); this'll probably relate to the geometric connection. I can see that I'll need some study. Thanks for the connection. —Quondum 19:16, 25 March 2014 (UTC)

I also wondered about quadratic forms, but the second axiom gave me pause: and (Q(x+y)-Q(x)-Q(y))/2 is a bilinear form. Yes, the Clifford and Weyl algebras are over fields. What I mean is, take a sesquilinear form over a division ring and try to make a Clifford-Weyl style algebra out of it. There are a lot of things to watch out for. For one thing, I guess we need to consider V as a left-and-right vector space, so that the tensor powers can be constructed. I'm not totally sure if the "tensor algebra" built this way is satisfactory. If it does turn out to be a ring, we should be able to quotient out by the right elements again to get a 2^n dimensional left-right-vector-space-ring. There are probably even other complications I'm overlooking in my haste to type this. Rschwieb (talk) 19:52, 25 March 2014 (UTC)

@Q: I have raised the question about the definition of vector space over at Talk:Vector space. At least two major references allow for non-commutative fields. These are also the only references I've read not being "physics" or "undergraduate", so I'm pretty sure that the majority's view on what a vector space really is isn't up to date (just like the view that thingies with length and direction that can be added and multiplied description isn't). This is, of course, immaterial, I'm fine with calling vector spaces over non-commutative fields for banana spaces. YohanN7 (talk) 20:21, 25 March 2014 (UTC)

And, of course, (remember the Maschen transform), the (right) "vector spaces" over non-commutative fields are henceforth called Quondum spaces :D YohanN7 (talk) 20:25, 25 March 2014 (UTC)

Slightly more seriously, here is what I'm working on: User:YohanN7/Classical_groups. The page has a (so far empty) talk page. Please feel free to comment. I've just begun. YohanN7 (talk) 20:30, 25 March 2014 (UTC)

@Y: Using "vector space" for a module over a division ring is common practice in abstract algebra. Why do all the linear algebra book use fields then? Well for one thing we don't get tripped up when we hit bilinear forms, and for another things are just simpler with commutative rings, and finally fields take care of a huge portion of what linear algebra is used for already. It is not often that a linear algebra student needs to work over a ring that isn't a finite field or a subfield of the complex numbers. Yet another wrinkle contributing to this terminology is that "field" has been used to mean "division ring" historically. The wiki article on fields confirms this, but it's not very detailed. This usage may be confined to one or two languages only (I have French in mind.) Rschwieb (talk) 13:12, 26 March 2014 (UTC)

Thank you for your clarifying remarks. My point is solely to get in a sentence (at the most two) in the affected articles to reflect the fact that there are generalized definitions in practical use. I don't want to change the "main" definition of (for instance) what a vector space is. It is also common practice in Wikipedia to mention alternative definitions when they exist. From a practical point of view, this would also reduce the chance of meaningless debates over terminology, like here, Talk:Vector_space#Definition. YohanN7 (talk) 14:14, 26 March 2014 (UTC)

Good head on your shoulders :) Rschwieb (talk) 16:33, 26 March 2014 (UTC)

The Barnstar of Diligence

This not a trivialization.

		The Barnstar of Diligence
		For all your work on the Lorentz group and related articles. Excellent work! M∧Ŝc2ħεИτlk 19:03, 10 April 2014 (UTC)

Mathsci

You might like to know that Mathsci was banned from Wikipedia by the Arbitration Committee and should not be editing at all. Starting a discussion with him on his talk page is encouraging him to break the terms of that ban (again) and will probably result in his eventual return to productive editing, if ever, being delayed even further. Deltahedron (talk) 20:26, 21 April 2014 (UTC)

I was aware of that. The ban doesn't include answering direct questions on his talk page as far as I could see. I'm also sure he has the judgement to refrain from answering if he himself feels that he is breaking the terms of the ban. It might have been different if he was the one contacting me, asking me to make changes according to his wishes. I contacted him because the section of the article in question is obviously written by someone well acquainted with the subject. YohanN7 (talk) 21:10, 21 April 2014 (UTC)

Wikipedia:Banning policy: An editor who is site-banned is forbidden from making any edit, anywhere on Wikipedia, via any account or as an unregistered user, under any and all circumstances. The only exception is that editors with talk page access may appeal in accordance with the provisions below. In this case, Mathsci explicitly acknowledged "the terms of WP:BAN disallow banned users, even if they are experts on the subject, from making any kind of comments" and "I will not use my talk page to make comments on how articles are being edited". I would be happy to see Mathsci return to mathematics editing provided he can do so in a constructive and collegial way (although I have not had the latter experience with him in the past) since he is indeed an expert in his area. Encouraging him to violate those assurances is likely to delay any successful appeal. I might add that however expert he may be, you do not need to ask him for permission to make any edits and the best place to discuss the way to improve an article in on the article talk page, not on any user's talk page, banned or not. Deltahedron (talk) 21:26, 21 April 2014 (UTC)

I just read your posts here. I didn't know that you were personally involved. I prefer to just stay away from the whole thing, leaving just one observation behind:

Most of these conflicts are taken far too seriously!

It's not the second world war goddammit.

I will not ask Mathsci anymore questions unless I really want to for some reason. I'm not banned. Also, he has not commented on how the article in question has been edited. He has not been breaking the terms of his ban in that way at least. YohanN7 (talk) 21:32, 21 April 2014 (UTC)

Fair enough. Deltahedron (talk) 21:38, 21 April 2014 (UTC)

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Why did you undo my changes to Naive set theory?

Why did you undo my changes to Naive set theory? I've reasoned them in the talk page of the article. 79.252.242.192 (talk) 13:42, 4 May 2014 (UTC) Thomas Limberg (Schmogrow)

See the talk page. YohanN7 (talk) 13:43, 4 May 2014 (UTC)

Thank goodness we won't have to deal with that user again for a while... Rschwieb (talk) 23:48, 11 May 2014 (UTC)

Haha, yeah. But I feel sorry for him, I honestly do. I think he is sick (needs treatment), and that he had no intention of vandalizing or whatever. He just seems to think he is the prophet of mathematics, for real.

The Germans were much more effective. He lasted only hours there, and he didn't even insult anyone, Just made a couple of confused posts. He also linked his talk page here to the Naive set theory talk page there, asking for support. Not smart.

I learned something. The next time, I'm not going to try to discuss rationally. Partly because it's tiring and partly because it makes me look bad. (I think the move proposal could have been taken more seriously if I had ignored him, there was some support for the idea. (Trovatore found it plausible at least.) Besides, it's a bit immature on my part to not to just let go. Unfortunately, I can't possibly blame it on my young age. YohanN7 (talk) 00:05, 12 May 2014 (UTC)

Hah, well yes, this is the sort of situation one can learn valuable lessons from. I certainly remember an exchange like this one editing here, and similar ones arising from conflicts at math.stackexchange. It really is a college course in figuring out what to do with difficult people. Rschwieb (talk) 13:34, 12 May 2014 (UTC)

Why did you delete the 'Humanities' section in the 'Topology' page?

I can't see why this section has been removed. It makes perfectly sense to me, as it gives readers an idea of the practical application of topology in the Humanities (a reference that was regrettably missing in the page), providing also some useful reference, in the hope that new editors could integrate (rather than delete) the section. It seems to me that your comment that the section and the last sentence are 'nonsense' is completely unjustified. As far as I know, Lacan was well-known to use topology in his psychoanalitic theory of the unconscious. — Preceding unsigned comment added by Sesamo12 (talk • contribs) 08:40, 26 May 2014 (UTC)

Your submission at AfC Closed subgroup theorem was accepted

Closed subgroup theorem, which you submitted to Articles for creation, has been created.
The article has been assessed as Start-Class, which is recorded on the article's talk page. You may like to take a look at the grading scheme to see how you can improve the article.

You are more than welcome to continue making quality contributions to Wikipedia. Note that because you are a logged-in user, you can create articles yourself, and don't have to post a request. However, you may continue submitting work to Articles for Creation if you prefer.

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Thank you for helping improve Wikipedia!

Huon (talk) 17:25, 16 July 2014 (UTC)

DYK for Closed subgroup theorem

 — Crisco 1492 (talk) 15:08, 2 August 2014 (UTC)

Your uncivility

I find your behaviour uncivil. This is the second time in a short interval that you have personally attacked me, in contravention of WP policy, and without apparently reconsidering and retracting your statements. Whether you consider your claims to be true or not, there are limits to acceptable behaviour. The following are statements that you have made:

• "Once again you are arguing about a subject you don't know anything about."
• "You do not understand because you are mathematically (and otherwise) immature."

Would you like to acknowledge that these statements are not within the spirit of Wikipedia, or would you prefer the alternative of opening up the matter to broader community scrutiny? —Quondum 05:48, 29 July 2014 (UTC)

Oh, like if any of these two comments of mine weren't so very well deserved by you?.

Somebody needs to tell you sometime. Now I have told you – and you have told me. Relax. YohanN7 (talk) 08:20, 29 July 2014 (UTC)

Whoa! Lots of excitement! YohanN7: at times I've said something similar to Quondum. I think this is largely due to his willingness to try out ideas without being an expert in the field. But he does not pretend he is more of an expert than experts, and ultimately he is cooperative and listens well. In many discussions like that I've found I've learned a lot from his fresh viewpoints, and I can tell he's certainly learning a lot from me too.

Quondum is probably going to be one of the best non-professionals you collaborate with here. Yes, he's going to say things that a mathematician might not say, but that is to be expected: there are many nonprofessionals on Wikipedia, and the last thing we want to do is to slap them silly with claims to professionalism whenever they speak up. What's important is that he acknowledges his limits and collaborates well.

This being the case, would you consider retracting the statements? They don't really reflect well upon anyone or the community. And as you said, both of you have gotten messages across to each other :) This would probably be the most sensible resolution, right? Thanks for reading: Rschwieb (talk) 13:15, 29 July 2014 (UTC)

Thanks for dropping by at the right time. The nature of Quondum's posts have gradually changed the last year or so. As he gets more knowledgeable, his confidence grows, which is fine. But this has unfortunately also resulted in that he does sometimes come across as someone pretending to be an expert. He has on several occasions presented his ideas (not always Nobel prize winning ideas) in a way that hints that the other people in the discussion (read me) are pathetically wrong. This has developed into a behavioral pattern, and he winds his messages into ever more elaborate English. The last incident clearly shows this (if you care to read it all). Quondum is lecturing all the way, and then infuriated "leaves the thread" dropping links pointing me out behind him, once more hinting that I'm pathetically wrong, not worthy discussing with, because I'm silly enough to believe the geodesic equation is relativistically invariant.

I will probably retract my statements officially, but I want to hear first what he has to say about what I just wrote. YohanN7 (talk) 14:19, 29 July 2014 (UTC)

I know what you mean, and I can say with nearly 100% certainty that I've corresponded with him more than you have. (The emails and notes would probably fill a 100 page book by now, at the very least.) You don't have to take my word for it, but I would say that I'm glad I allowed him leeway in our discussions. It has always turned out well in the long run. This is a good skill to cultivate when working collaboratively on the internet anyway :) Try to save any frustration you might have for the destructive incompetents who really deserve to be deflected.

Finally, I hope Quondum doesn't mind how much I've had to talk about him in the third person. I hope none of this seems like a back-handed compliment. Rschwieb (talk) 17:10, 29 July 2014 (UTC)

-

While I am happy to acknowledge that I come across as bombastic/overly assertive/lecturing, i.e. that I express my perspective too strongly, the issue that I have raised here is that you have turned expressing ourselves on a topic into a personal attack. Your insistence on analyzing the justification for your attack before even acknowledging it shows that you seem to have missed this point. My intention is most certainly not ever to belittle you. Note how JRSpriggs, who would have been the natural target (having provided the equation) of any slight, responded informatively and at the level of the subject matter.

When I challenge what you say, please do not interpret that as an attempt to belittle you or claim superiority. There is no shame in being wrong, as I clearly have been and will again be on many occasions. What is at issue is how we treat each other. Perhaps you are overly quick to interpret challenges of the ideas being discussed as a criticism of you? And perhaps this is making it difficult for you to listen to what I'm actually trying to get across at the technical level? —Quondum 21:35, 29 July 2014 (UTC)

When you have challenged what I say, then there has been times (several) that I have interpreted it as attempts of just provoking me for the fun of it. In response to such things, I have even accused you once of trolling (remember that particular occasion?). When you manage to squeeze in four or five serious errors into just a couple of sentences (not talking about spelling or grammar here), along with insinuations, then it is easy to believe that you are just being purposefully provocative. I think nobody is that incompetent. Now you deliver critique against me defending why I have been nasty against you in a couple of posts (hinting that it is irrelevant why). Well, even in murder cases, the court will be interested in the motive before sentencing. YohanN7 (talk) 13:23, 30 July 2014 (UTC)

I remember an occasion when nearly my entire post had to be retracted, but that was in response to Incnis. As I've said I've made many mistakes, but none of them have been intentional mistakes. The two of us have had a lot of contentious interactions in the past. Since you wish to retain your view on my motive, for both our sanity I must ask you to refrain from asking for my comment, contribution or collaboration in future. Why you have done so in the past mystified me: in essentially every instance the topics have been vastly beyond my understanding, and I've not pretended otherwise. What is clear is that I cannot place any reliance whatsoever on you to assume good faith. —Quondum 14:56, 30 July 2014 (UTC)

I have asked you for comment, contribution or collaboration in the past because it has been valuable, much more often than not. No mystery there. None of us particularly like being wrong when it comes to hard facts in math and physics. We are both wrong on occasion, but I think I handle being wrong better than you, not because I'm inherently better, but because I'm (with 90% certainty) older, and in that particular way (and only that way) wiser than you. When I was, say, a junior or senior undergraduate (the stage at which knowledge increase w r t time is steepest) I was Quondum squared. You deliver two incompatible messages. On the one hand, you are "happy to acknowledge mistakes". On the other hand, you write your posts in a lecturing tone, including in subjects which you admit that they are "vastly beyond you understanding". Don't you see that this practice of yours is against the spirit of any sort of civilized behavior, whether or not you can find a WP:THIS or WP:THAT supporting the point? YohanN7 (talk) 15:48, 30 July 2014 (UTC)

@Yohan7 : Speaking as one who knows Quondum relatively well, and who has only read the comments made on this page without getting steeped in the history that led to them, I need to say you're the one coming off as more negative. Don't misunderstand, I get that previous history of interaction can let one feel justified in saying some things, and I'm not accusing you of anything. But we all have to try our best to break free of history sometimes. There is basically an olive branch being extended in the paragraph previous to your last response, but seeing as the antagonism continued after that paragraph, I think it slipped under your radar. Easy to do.

Let's all just let things mellow for a while, and when we all meet again we'll apply what we learned here while giving each other clean slates. I've had this sort of experience a couple times here and on related sites, and I can guarantee the clean slate thing works out pretty well almost every time. Rschwieb (talk) 15:41, 30 July 2014 (UTC)

I was once mad at somebody for 72 straight hours. Don't think I'll break that record this time . YohanN7 (talk) 15:48, 30 July 2014 (UTC)

Q: Would you consider a truce? When reading my own posts, I'll have to reconsider my own maturity. The whole ting is really a silly little argument over (close to) nothing. You and me collaborating (and sometimes seriously debating) is worth a lot. YohanN7 (talk) 14:45, 31 July 2014 (UTC)

Truce? As in terminating hostilities, yes. And your more relaxed position is appreciated. However, this does not mean that any of the underlying issues have actually been dealt with: there are several disagreements on fact that we'll have to accept, and I'm not going to be interested in reengaging in interaction that I feel could lead to the same cycle again; we both still have the same buttons that can be pushed. I imagine I'll do well to learn from this and avoid engaging in topics for which I do not have authoritative references to fall back on (not only with you), as well as being more thoughtful in how I engage others. And yes, the original arguments are relatively unimportant: I am not invested in the accuracy of WP enough to engage in battles about it. —Quondum 22:48, 31 July 2014 (UTC)

Have we now gotten past our little argument? I'd like to see us constructively work together again, and I admit uncivil behavior. I have a bad temper, but the anger never lasts. YohanN7 (talk) 07:31, 23 August 2014 (UTC)

Putting it behind is was what my previous comment was meant to mean, and that I'll attempt to anticipate and manage repeat events. —Quondum 14:59, 23 August 2014 (UTC)

A barnstar for you!

	The Citation Barnstar
	Hi Thank you for reverting my mistake. I was using energy momentum tensor written in this page which is not devided by c^2: https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor I think these two page have a conflict in definition! Is that true? Best regards , Issa Eghdami Issaeghdami (talk) 16:06, 30 August 2014 (UTC)

I think you have a point, and Electromagnetic stress–energy tensor is correctly given in SI units. There is also the connection

$c^{2}={\frac {1}{\mu \epsilon }}$

so there seems to be something wrong. @JRSpriggs:, what do you think? The reference MTW certainly doesn't give what is in Stress–energy tensor, besides, it uses different units. YohanN7 (talk) 17:03, 30 August 2014 (UTC)

Both MTW and Landau & Lifshitz give the T⁰⁰ in CGS units as correctly presented in Electromagnetic stress–energy tensor. YohanN7 (talk) 17:48, 30 August 2014 (UTC)

Why did you undo my edit on Maxwell's equations?

Dear YohanN7,
My addition was historically correct and commensurate with other wikipedia articles on the topic! Why did you undo my edit, therefore? Please explain.
Regards,
Bkpsusmitaa (talk) 18:12, 2 September 2014 (UTC)

It might be worth a footnote in the history section (if you can source it), not a large (and POV, it din't read well) chunk in the lead. I suggest you bring this up on the articles talk page if you want it in. Here is not the place to debate it. Best. YohanN7 (talk) 18:33, 2 September 2014 (UTC)

From a little google research, I found the hyphenated term is only marginally used. (Compare 34k hits vs 500k+ hits.) On top of that, many of the hits at the top of the search for "Maxwell-Heaviside" were pseudoscience sites. This leads me to believe that it is not an appropriate term for WP. User:YohanN7 I notice that the "Maxwell-Heaviside equations" were also inserted into History_of_Maxwell's equations at some point. If it is truly this marginal, the hyphenated term may well deserve to be eradicated from that article. I'll leave that suggestion to people more familiar with that literature, though. Rschwieb (talk) 18:37, 2 September 2014 (UTC)

And the main reference seems to be Myron Evans... I suppose you know who it is. He is the most untrustworthy person in the universe when it comes to naming equations, see Einstein–Cartan–Evans theory. Yes, Evans himself christened it that way himself. (Hope I don't confuse him with somebody else, but according to Amazon, it's the Myron Evans.) YohanN7 (talk) 19:05, 2 September 2014 (UTC)

Thank you for responding. What about Myron Evans? I have quoted the original wikipedia article Oliver Heaviside. Anyway, moved the discussion to the main article's talk page. Bkpsusmitaa (talk) 18:00, 15 September 2014 (UTC)

More refs

Hi YohanN7, sorry to cut in randomly like this after such a long absence, I'll be back in business soon, but in case you do not have some/all of these refs, they're on Q's page. Best! M∧Ŝc²ħεИ_τlk 07:31, 19 August 2014 (UTC)

Good to see you active again! YohanN7 (talk) 08:10, 23 August 2014 (UTC)

In case you haven't seen these:

• Yoshio Ohnuki's Unitary Representations of the Poincaré Group and Relativistic Wave Equations is a detailed book on relativistic wave equations that actually discusses in some depth higher-spin and even continuous-spin particles, massless and massive, and tons more. The author looks quite authoritive, apparently one of the Japanese physicists who has contributed to group theory in particle physics in the 20th century. Only recently found this, may get it soon. What worries me is that, despite the competence of the author, there could be potentially many typos in this incredibly dense and hyper-detailed exposition.
• Recently found Quaternions, Clifford Algebras and Relativistic Physics by Patrick Girard. Looks like a promising source on quaternions in physics, especially relativistic mechanics and EM. Haven't bought it.
• Gauge Theories in Particle Physics by Aitchison and Hey is an authoritive particle physics 2-volume work. The 4th edition came out recently and discusses the new experiments of the Higgs. I don't have any edition.
• Theres a bunch of books which include (as authors or co-authors) the notable Russian mathematicians Kolmogorov and Shilov, on linear algebra and analysis (nice examples include Integral, Measure and Derivative: A Unified Approach by Shilov and Gurevich and Introductory Real Analysis Kolmogorov and Fomin), which I still havn't bought yet...
• A brilliant choice is Altmann's Rotations, Quaternions, and Double Groups (Dover edition). Covers loads of associated topics with the title - spherical vectors and tensors, spinors, rotation matrices and relation between angular momentum operators (for both integer and half-integer quantum numbers), some group theory and representation theory, etc. Much of the formalism uses Dirac notation. Bought this recently - seems like an invaluable reference.

P.S. Thanks once again for the reccomendation to Stephen Willard's General Topology - it's brilliant. Some of it is over my head, some looks familiar. Best, M∧Ŝc²ħεИ_τlk 07:17, 14 September 2014 (UTC)

It has the best (and proportionally largest) collection of problems I have ever seen. It is a pleasure just reading the problems and the accompanying detailed hints. General topology is also a topic that is absolutely unavoidable at the graduate level, mostly in math, but also in physics with functional analysis and manifold theory (not to mention group theory) becoming more important. YohanN7 (talk) 20:07, 15 September 2014 (UTC)

One more ref in case you're unaware, after this I'll stop cutting in: Theory of Spinors: An Introduction by Carmeli and Malin. The contents in the preview looks very impressive: covers group theory for SO(3), SU(2), SL(2,C), Lorentz groups etc., and applications in RQM, EM, and GR. Moshe Carmeli seems authoritive as an author.

Maybe you'll like it. For me, it's for a distant-future invesment... M∧Ŝc²ħεИ_τlk 21:32, 15 September 2014 (UTC)

Wavepackets in quantum mechanics: Remove rejection statement at top?

Thanks for your help with a novice user's draft of the article on wavepackets. One question: Would be OK to remove the rejection notice at the top?--guyvan52 (talk) 14:43, 10 November 2014 (UTC)

No, I don't think so. It hardly matters, but pretending that an article draft is not reviewed before is unlikely to improve its chances. If it is improved with references (the explicit reason for rejection), then it is unlikely to be rejected once again for the same reason. It may be rejected for other reasons (I can supply a few). I don't think it is ready for man space yet. See Draft talk:Wave packets in quantum mechanics. As an aside, to where is it actually submitted? To Wikipedia Main Space or to Wikiversity? It seems very much to be submitted to Wikipedia main space. YohanN7 (talk) 19:47, 10 November 2014 (UTC)