Talk:Scalar field theory

new page

I've started this new page on Scalar field theory, which no longer just redirects to scalar field. I've done quite a bit myself, but any help from other physicists would be useful and appreciated.--Jpod2 11:15, 19 September 2006 (UTC)

Merger with quartic interaction

Many of the same topics were duplicated under quartic interaction, which included a lengthy canonical quantization discussion which seemed out of place there, so I moved it here. Since most of the topics here were duplicated there, I took what I thought was the best of both and merged them. Overall, this was the better article to begin with. The feynman integral section is entirely rewritten, following Ramond's text, mostly. I thought this was necessary because the earlier version lacked detail, and neither the path integral formulation article nor the Feynman graphs article is very illuminating. (To be fair, trying to explain these in such generality is daunting.) I also shortened the triviality section a little, since there are already fairly good articles on quantum triviality and the Landau pole. Dusty14 (talk) 01:06, 16 May 2010 (UTC)

References

There is a request for documenting the material here, which I think is reasonable. I tried adding some inline references to the parts I added. I'm not sure where the rest is from, but it seems pretty standard. Perhaps someone could be more specific about where each section originated? Also - are you certain that there is no rigorous proof of φ⁴ triviality in 4 dimensions? I thought I remembered seeing one a few years after Aizenmann's in D > 4, perhaps 1984 - 1985? I can't remember who, except that it might have been a German. If the statement about the lack of a proof cannot be supported by a reference (or someone who would clearly know), I think it should be removed. I'll be checking to see if a reference is posted. Dusty14 (talk) 01:14, 16 May 2010 (UTC)

About triviality in d=4, there is currently a lot of activity. There is some published material

http://arxiv.org/abs/hep-th/0611276

but mostly is appeared in arxiv quite recently:

http://arxiv.org/abs/1003.3670

http://arxiv.org/abs/0804.0368

http://arxiv.org/abs/0802.1183

Here, with different approaches, authors prove that the beta function for a quartic scalar theory goes like $d\lambda$ and so the running coupling goes to zero at lower momenta. Then, the theory is proved to be trivial. I tried to put this material into this article but an editor promptly removed it. My view is that, at least for a couple of these works, one has a rigorous proof. Others papers give a really sound support to such a conclusion.

Let me add my compliments for your very good improvement of the article.--Pra1998 (talk) 13:26, 19 May 2010 (UTC)

Confusing

Somebody who can explain this topic to his grandmother has to write at least the intro so EVERYBODY knows what it is about and not just the ones who already know what it is about.

Explaining one unkown thing (Scalar Field) with another (Vector Field) is F(ailed)! The whole article is useless and should be deleted as it violates the Wikipedia guidelines. This article has to be moved to a Professional Wiki like Physics- or MathWiki. — Preceding unsigned comment added by Jangirke (talk • contribs) 09:36, 3 October 2013 (UTC)

I fear you are underestimating somebody's proverbial grandmother so condescendingly abused. If said grandmother insists on proceeding past the "in theoretical physics" gate, she may well get something out of this. But it is not true that all highly technical subjects in WP have to be instantly comprehensible to somebody with no training and bring her up to speed in a few pages. WP is meant to illuminate a broad and motivated audience, and deleting the article as you propose will help neither your notional grandmother nor the interested reader who evidently gets something out of it, such as a beginning graduate student in physics ---they come by the dozens every day, if you consulted the traffic stats. I doubt they all leave in as abject and helpless a huff as you seem to have. Cuzkatzimhut (talk) 16:33, 13 August 2015 (UTC)

Scale invariance implies conformal invariance??

The sentence "In fact, the scale-invariant theories in the previous section are also conformally-invariant." seems to imply that scale-invariant theories are also conformally invariant. To me this seems like it's the wrong way around: something that is invariant to all conformal transformations is also invariant to all scaling transformations, as those form a subgroup, not the other way around. Jaspervdg (talk) 08:54, 25 June 2014 (UTC)

Indeed, counterintuitive as it might be, in some cases the part suffices to argue for the whole. E.g. in d=4, a unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. Cuzkatzimhut (talk) 15:55, 28 December 2014 (UTC)

Nonlinear (interacting) theory

In this section, and a few that follow, the mass term is making sporadic, but not consistent, appearances. Why wouldn't there be a mass term? It can always be eliminated if desired by setting m² = 0. YohanN7 (talk) 09:53, 13 August 2015 (UTC)

An additional mass term is not necessary, as it is the quadratic piece of the potential V, as exemplified already. There is no point in adding an extra term and then merging it with the V piece. Cuzkatzimhut (talk) 10:30, 13 August 2015 (UTC)

That makes sense, except that it says that V typically is a monomial of degree 3 or higher. YohanN7 (talk) 10:55, 13 August 2015 (UTC)

Oops! had missed that one. The polynomial degree casuistry is superfluous! The generic nature of the polynomial is displayed in the formulas that follow! Thnks....Cuzkatzimhut (talk) 16:07, 13 August 2015 (UTC)

Strange statement and ref in opening paragraph

"Thus, scalar field theory is closely related with quantum field theory." What does that mean? The first sentence already states scalar field theory is a special class of classical or quantum field theories. What does this second sentence tell the reader? How is a review article on a different specialized subject meant to steer the reader to QFT, a huge vernerable subject? Cuzkatzimhut (talk) 15:44, 13 August 2015 (UTC)

Recently, there was this vague and synoptic part in the lede, Because of the relative simplicity of the mathematics involved, scalar fields are often the first field introduced to a student of classical or quantum field theory. However, I removed the part now entirely, but this could be added with some better reference and rewording under the general section. prokaryotes (talk) 15:52, 13 August 2015 (UTC)

It looks quite good to me, but, if you can improve it, in acceptable english, you might well reintroduce it. The statement is self-explanatory and needs as much referencing as the ability of fish to swim in water. Scalar field theory is the simplest prototype of QFT, since it eschews Lorentz or spinor index complications, polarization states, etc... The outside reader might have something like this explained to them, if it is not already evident. Cuzkatzimhut (talk) 16:01, 13 August 2015 (UTC)

The part about math is subjective, dependent on the readers education, the part was uncited too. If you look above readers already complained about the technical scope of the article. As mentioned we can add such info on education/teachings but it requires a reference. prokaryotes (talk) 16:04, 13 August 2015 (UTC)

Of course, people expecting to understand something they were not trained for will always complain they cannot grasp something instantly. If you think there is a particularly pithy reference to explain the obviousness of the statement, sure, go ahead, add one, provided it helps instead of hijacking eyeballs for a review article on an irrelevant subject purporting to illuminate that very narrow statement we are discussing here. Cuzkatzimhut (talk) 16:11, 13 August 2015 (UTC)

If you want to add to the article feel free to do so, but make sure to back up any additions with a reliable source. prokaryotes (talk) 16:14, 13 August 2015 (UTC)

The sentence (whether modified) belongs in the part of the lead that explains what scalar field theory is good for. It can be referenced, see e.g. Franz Gross RQM/QFT. He uses it as the first example in three different chapters for pedagogical purposes, not because there are a host of elementary scalar fields around. You should not remove material that is both obviously true and possible to "source". Replacing general references with recent review papers on the going "Beyond the Cosmological Standard Model" is not helping the perplexed, nor is removing standard declarations of which conventions are used in this article. YohanN7 (talk) 16:17, 13 August 2015 (UTC)

Now also statements "two levels down" are being removed because of lack of citations. You misunderstand the guidelines. You are supposed to use your judgement, not remove material because you think you can. (The fact that spin 0 particles are bosons can be found in any and all of the references.) YohanN7 (talk) 16:31, 13 August 2015 (UTC)

Hello Yohan, i have no doubt about that, since i cited this in my edit summary. However, the entire sentence was at issue. Feel free to improve the part with the required reference if you deem it missing. Additionally i ask you to back up any of your edits with a reference. This is 101 of WP. prokaryotes (talk) 17:11, 13 August 2015 (UTC)

Content changes

OK, let's argue here, "nicely" without peremptory reverts as of this morning's, what ws confusing about the explanation of what a scalar is. To me, at least, even though I don't have strong opinions, explaining out bosons is at the heart of what their field theory is all about. Moreover, all the meticulous reference improvements were also summarily negated, in the same move. How about freezing things as they stand now, and try to see what troubles one, in this case the reverter? The additions in the lede appear inoffensive and explanatory to me. How would a bit more background information be declared "confusing" and hurt? The referencing is impeccable, no? Cuzkatzimhut (talk) 18:45, 19 August 2015 (UTC)

Suspect vandal already at ANI whining. I removed one sentence of gibberish of his and a totally irrelevant "reference". He removed, in turn real content (1k bytes) referenced by real references. YohanN7 (talk) 18:50, 19 August 2015 (UTC)

I second my agreement with the removal of the Tegmark et al cosmology reference. As I already indicated last week, any undergraduate could instantly identify it not as a seminal reference on scalar QFT, but rather a gravitational physics review: the purported diversion on galileons is, frankly, a red herring, as quickly identifiable by the majority of the readers, who would only roll their eyes once they understood what is being referenced: higher derivative theories? is this for real? Cuzkatzimhut (talk) 19:06, 19 August 2015 (UTC)

Very sad to see a crank coming out from the blue, vandalizing a scientific article and claiming she is right. I do not know how you could dispose of such a joker.--Pra1998 (talk) 19:31, 19 August 2015 (UTC)

No, it is not for real, because I think the vandal would have reverted every any any edit of mine. In fact, I am almost entirely sure he never read it. As for the reference I removed, it is a "perfectly normal paper" (except it is l-o-n-g), but certainly not dedicated to scalar field theory. The whole thing is just a set-up. YohanN7 (talk) 19:18, 19 August 2015 (UTC)

• Comment The Tegmark paper serves as an example for the usage of scalar fields, and the recent edits by YohanN7 also removed some structure from the article and his edits lack references. Additionally the lede is to long again. prokaryotes (talk) 19:20, 19 August 2015 (UTC)

Don't lie. You can lie when you cry at the ANI, but not here. My edit did not lack references. YohanN7 (talk) 19:48, 19 August 2015 (UTC)

The lede explains to the outsider what on earth it's all about. Applications can go to the bottom, in a section called applications, provided the text is not unsound, like the wording reverted, which certainly did not even suggest applications!?? What, exactly, are we talking about here? In any case, I would not object to an unobtrusive irrelevant reference at the end of the article---I guess intelligent, well-meaning readers could easily shrugg it off, or yank it out or replace it themselves. WP is a collective enterprise, after all. Cuzkatzimhut (talk) 19:37, 19 August 2015 (UTC)

However, Cuzkatzimhut in your recent edits on the article you had no problem with my edits, you even edited them. Now suddenly when YohanN7 removed my edits you start complaining. Notice that the issues now dozens of times mentioned, in particular to poor references will not be resolved with reverting or battleground behavior. prokaryotes (talk) 19:47, 19 August 2015 (UTC)

Flawed syllogism: I already objected to that reference above. It is not true that anything I do not revert I wholeheartedly agree with. I left the silly reference alone to "Keep the peace" and prevent precisely this recursive tendentiousnes; but, in retrospect, I may have made a mistake, inviting further bullying. For the life of me, I do not understand why you seem to have such a stake in that reference. But, didn't we already agree that YohanN's referencing of today is impeccable? What is the story? Why? WHY? Cuzkatzimhut (talk) 19:54, 19 August 2015 (UTC)

Here is a novel idea, prokaryotes: This is a talk page for an article. Why don't you propose a brief section on "Applications" to go to the customary bottom of the article, on this very page, the proper forum. If it is sound and passes muster in the community, why, I'd be supportive in letting it into the article; and I'd even try to contribute small tweaks to help it make better sense. Otherwise, YohanN's conviction that all this fuss is part of a setup will not be contradicted. Last week, on the FGR article, you found the secondary reference that satisfied you, and terminated a needlessly acrimonious "attrap" debate. So, why don't you be constructive and actually put in the work to propose something (beyond the bizarre "General" gig!) that could impress everybody well with its good sense? I mean the article is a collective effort, no? Cuzkatzimhut (talk) 22:14, 19 August 2015 (UTC)

The general section was a good starting point for general infos on SFT. The term "General" is a common naming within related articles, the usage of the name Applications is new to me. However i wouldn't necessarily object to a different name, but sections are important to improve overall readability. The Manual of Style/Lead section - Provide an accessible overview explains "In general, introduce useful abbreviations, but avoid difficult-to-understand terminology and symbols. Mathematical equations and formulas should be avoided when they conflict with the goal of making the lead section accessible to as broad an audience as possible." However, currently the lede is a little to much into theorem (links to here). This might be okay for people who study the topic indepth, but not for a general introduction. Thus i would keep "A scalar field is invariant under any Lorentz transformation", including a reference for this, currently reference might be considered okay but hard to follow up with 2 notes in the lede. Improvements to the lede could include a link to Higgs boson, from whom SFT originates, and a quick explanation with some simple examples when it is used (Minkowski space, but as simple as possible, i.e. "barring over-riding reasons", is not a way to write something simple). The lede as it stands now is to technical. Notice it wasn't very good with my edits either, but improved after the removal of a reference list, and the mentioned start with moving content to a new section.prokaryotes (talk) 22:58, 19 August 2015 (UTC)

"Applications" is common in physics articles, near the end. It is the optimal format here. Propose your paragraph. If you are looking for Higgs connections here, for god's sake, go to spontaneous symmetry breaking, not SFT!! (But you could mention Higges in the applications, too.) The top heavy Lorentz properties could go into a footnote which YohanN is very good at. I stuck "barring over-riding reasons" to mitigate this gratuitous Minkowski stuff, which would elicit sneers from someone knowledgeable. Field theories are defined in all types of spaces, including Euclidean ones, as in critical phenomena, and, indeed, sometimes the base space is not even a space-time. The whole fuss about Minkowski spaces was not there before the damage started. Just propose full paragraphs. Here. I think the chapter and verse and manuals could wait for the arguing about them. Cuzkatzimhut (talk) 23:13, 19 August 2015 (UTC)

Of course the Minkowski stuff was there, all the time. DIF But when i try to improve the article according to style guides, make mostly layout edits, you accuse me of damage, or YohanN7 goes so far to call it vandalism. This is not the discussion environment which is needed at Wikipedia, or helps with a community afford. prokaryotes (talk) 23:21, 19 August 2015 (UTC)

No, you misunderstand, grossly: what was there was the fact that the +--- Minkowsi metric was utilized in the explicit discussion below. Not, repeat, not the odd statement that scalar field theories in general are defined in Minkowski space. (That was so wrong-minded I tried to stick in an admittedly forced deniability clause.)

But, in any case, this is not a flame forum about you, or me, or the past, or anyone's grievances, or practices, or manuals.

I gave you a way out: place your bets. Propose your explicit paragraphs here, take responsibility for them, and let the community discuss them. I don't believe the numerous page watchers need to think about anything else.Cuzkatzimhut (talk) 01:08, 20 August 2015 (UTC)

OK, after 36 hrs of insistent silence, I took under advisement all above comments as I understood them, moved technical statements to footnotes, and nixed the discursive pointless sentence which hardly says anything. I believe we are stable here for a while. Cuzkatzimhut (talk) 14:14, 21 August 2015 (UTC)

Possible error in "Quantum scalar field theory" section?

I believe there is an error in this article. I am not confident enough in my understanding to fix it.

In the section "Quantum scalar field theory", this article makes a number of definitions and statements, which cannot all be correct. Specifically, its claim about the commutator of the creation and annhilation operators does not match its definition of those operators.

The article claims that $\left[a({\vec {k}}_{1}),a^{\dagger }({\vec {k}}_{2})\right]=(2\pi )^{3}2E\delta ({\vec {k}}_{1}-{\vec {k}}_{2})$.

But using the article's definitions, and calculating:

${\begin{aligned}&\left[{\widetilde {\pi }}({\vec {k}}_{1}),{\widetilde {\phi }}({\vec {k}}_{2})\right]\\&=\left[\int d^{3}x_{1}e^{-i{\vec {k_{1}}}\cdot {\vec {x_{1}}}}\pi ({\vec {x_{1}}}),\int d^{3}x_{2}e^{-i{\vec {k_{2}}}\cdot {\vec {x_{2}}}}\phi ({\vec {x_{2}}})\right]\\&=\int d^{3}x_{1}\int d^{3}x_{2}e^{-i{\vec {k_{1}}}\cdot {\vec {x_{1}}}}e^{-i{\vec {k_{2}}}\cdot {\vec {x_{2}}}}\left[\pi ({\vec {x_{1}}}),\phi ({\vec {x_{2}}})\right]\\&=-i\int d^{3}x_{1}\int d^{3}x_{2}e^{-i{\vec {k_{1}}}\cdot {\vec {x_{1}}}}e^{-i{\vec {k_{2}}}\cdot {\vec {x_{2}}}}\delta \left({\vec {x_{1}}}-{\vec {x_{2}}}\right)\\&=-i\int d^{3}x_{1}e^{-i{\vec {k_{1}}}\cdot {\vec {x_{1}}}}e^{-i{\vec {k_{2}}}\cdot {\vec {x_{1}}}}\\&=-i(2\pi )^{3}\delta \left({\vec {k_{1}}}+{\vec {k_{2}}}\right)\\\end{aligned}}$

${\begin{aligned}&\left[a({\vec {k}}_{1}),a^{\dagger }({\vec {k}}_{2})\right]\\&=\left[E{\widetilde {\phi }}({\vec {k}}_{1})+i{\widetilde {\pi }}({\vec {k}}_{1}),E{\widetilde {\phi }}({\vec {k}}_{2})-i{\widetilde {\pi }}({\vec {k}}_{2})\right]\\&=Ei\left(\left[{\widetilde {\pi }}({\vec {k}}_{1}),{\widetilde {\phi }}({\vec {k}}_{2})\right]-\left[{\widetilde {\phi }}({\vec {k}}_{1}),{\widetilde {\pi }}({\vec {k}}_{2})\right]\right)\\&=(2\pi )^{3}2E\delta \left({\vec {k_{1}}}+{\vec {k_{2}}}\right)\end{aligned}}$

So something is wrong. A minus sign is missing somewhere.

73.71.23.246 (talk) 21:08, 7 June 2021 (UTC)