Talk:Quantum field theory

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This might be an unusual move, but sometimes its good to recognize excellent writing and remind each other why Wikipedia matters. This article has quite possibly the best physics writing I've read on Wikipedia so far. Its incredibly readable for a lay person like myself and has cleared up numerous holes in my knowledge without leaving me feeling like I'm shackled by my lack of formal physics and math education. Good work to all of you and thank you for this page. 2001:44B8:6117:B100:898E:A293:6AE6:817F (talk) 15:17, 2 November 2019 (UTC)[reply]

P.S. I just want to say that I couldn't agree more with the person who've written this compliment. [added by Koitus~nlwiki}

Wikipedia is the embodiment of the idea of scientific enlightenment! Thanks to the authors. [added by Interest in science]

A little late to reply to you, but thank you for the kind words! I undertook the task of writing a new article on quantum field theory after the previous version had to be deleted for plagiarism (and general bad writing). I had been an editor for a long time but never written a whole article myself, so it was quite a challenge. I'm happy you enjoyed it or found it useful. Please don't hesitate to improve it further or suggest changes. Yinweichen (talk) 22:30, 20 May 2022 (UTC)[reply]

Is there a set of ingredients that every QFT has? I sometimes see statements like "consider a QFT with the following property..." or "we will now construct a QFT with..." and I'm wondering what kind of object they have in mind. For instance, does every QFT have an underlying manifold, an action, a Hamiltonian, a Lagrangian, a Hilbert space, observables etc.? If so, what kinds of objects are these things mathematically? Thanks, AxelBoldt (talk) 02:50, 21 November 2011 (UTC)[reply]

If you can get hold of Stephen Weinbergs "The Quantum Theory of Fields" you would get a pretty precise view of what his view of what any QFT "must look like". Lorenz Invariance and the Cluster Decomposition Principle (distant experiments can't interfere) are Weinbergs main ingredients. There is a Hilbert Space, but Lagrangians (or Canonical Quantization of those) to obtain the QFT aren't set in stone. Even the renormalization requirement isn't set in stone (you'd have to read the book for that). YohanN7 (talk) 10:14, 12 September 2012 (UTC)[reply]

I just came upon:

Even though QFT is an unavoidable consequence of the reconciliation of quantum mechanics with special relativity (Weinberg (1995))

https://en.wikipedia.org/wiki/Quantum_field_theory#History

It is easy to construct a quantum relativistic theories of events, time-like rays, etc.; see p.75 of

http://alpha.math.uga.edu/~davide/The_Mathematical_Foundations_of_Quantum_Mechanics.pdf

Dave [email protected] http://alpha.math.uga.edu/~davide/ — Preceding unsigned comment added by David edwards (talk • contribs) 21:20, 3 February 2018 (UTC)[reply]

The non-existence of a wave function for a single photon is described here ^[1]. Sorry can not find the right way of editing this 'citation needed' — Preceding unsigned comment added by 112.202.19.32 (talk) 04:32, 5 March 2012 (UTC)[reply]

 Done thanks - MIRROR (talk) 17:34, 9 March 2012 (UTC)[reply]

(repost from WikiProject Physics) hi, i'm not sure if those articles really speak about the same thing. can someone tell me ? the paragraph Axiomatic approaches doensn't even mention the axiomatic QFT article. thanks - MIRROR (talk) 17:07, 9 March 2012 (UTC)[reply]

Layperson here, I'd just like to inform you that this opening sentence is worse than useless:

"Quantum field theory (QFT) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of degrees of freedom, that is, fields and (in a condensed matter context) many-body systems."

It's actually laughable how utterly opaque that is. Just so you know! :)

--24.5.197.145 (talk) 09:39, 6 July 2012 (UTC)[reply]

Glancing around I see that others have brought this up and you've responded, "WHAT?! WHICH!?!" So here's a good rule of thumb: If you need five blue links in just one sentence for terms which are essentially meaningless to a layperson, then you're not doing it right. At LEAST five different terms in that ONE sentence require extensive unpacking in order for it to make any sense. So yeah. WAY too much info. I'd need help with "parameterized," and especially "an infinite number of degrees of freedom." I also love how right after that particular meaningless word-salad, there's a little "Oh, to put it another way," and then a whole second utterly meaningless word-salad. Real quality :). — Preceding unsigned comment added by 24.5.197.145 (talk) 09:48, 6 July 2012 (UTC)[reply]

scuse me, six blue links; for terms which mean absolutely nothing unless you've majored in this subject. All of which require multiple page explanations. So, just to be clear, the lay person would need to go to each of those six pages, read everything there and then come back before they might have the vaguest most remote hope of understanding THE FIRST SENTENCE. Right, great writing boys. Just hope all this makes you feel fucking smart. --24.5.197.145 (talk) 09:11, 10 July 2012 (UTC)[reply]

Seriously folks, if you can't edit ANY part of this article into readability, why have it at all? Can't you at least provide a layperson's introduction? Or is the sole purpose of Wikipedia physics articles to provide undergrads with an intellectual circlejerk that can't be read by anyone outside their major?--24.5.197.145 (talk) 09:52, 6 July 2012 (UTC)[reply]

Although reading your comments really makes me laugh, what exactly do you expect? Quantum field theory is the most sophisticated physical theory we have, and even people like Witten acknowledge it as uniquely, notoriously technical. If you're that interested, go teach yourself the rudiments of undergraduate physics and come back in a few years. Michael Lee Baker (talk) 20:07, 3 November 2020 (UTC)[reply]

Sooooo should we label this article as being too technical and call it a day? Mizusajt (talk) 17:27, 24 August 2012 (UTC)[reply]

The preceding bunch of comments by 24.5 make me laugh! I'm a professional mathematician and even have a significant result in mathematical physics. I also am often frustrated when these physics articles are badly written and don't define their terms, not even in blue. I constantly hammer on about it, either complaining, or fixing, depending on my knowledge of it. Yet at the same time, I strongly recommend following those 5 blue links and reading those 10 or 15 articles. You'll range from the

nuclear spaces. It's the only way. 89.217.26.179 (talk) 07:52, 28 April 2015 (UTC)[reply

]

If I understand things better, I'll try to clear up the article. Count Truthstein (talk) 22:20, 15 December 2012 (UTC)[reply]

Any effort towards making this article more accessible and complete would be greatly appreciated. In my opinion, the material that is present is at about the right level (i.e., understandable to someone who has taken regular undergraduate QM), but it is very incomplete. Zueignung (talk) 22:34, 15 December 2012 (UTC)[reply]

To answer some of my own questions, the quantum field doesn't have a value at each point - there's the same nature of uncertainty in the value of the field at a point as there is with the position of a particle in ordinary quantum mechanics. It's an oversimplification to say that a type of particle is represented by a field permeating space-time. Neither is a physical state represented by an "operator-valued field" - the operators at particular points of space-time just represent observables, not the state of the system. The Lagrangian is used to describe the dynamics of a classical field, but that is not the whole story for the dynamics of the quantized field - either a path integral formulation can be used or a Hamiltonian operator can be derived. The expressions with creation and annihilation operators are not formal, but they could be depending on the formalism used to define Fock space - not that this matters as only the algebraic properties (commutation relations) matter.

As for what the states, operators and observables are, this will depend on the quantum field in question. The article

Concerning the "f*@!#~? useless" comments above, would a new article help? C.F.

Many of the criticisms above can be attributed to a difficult to understand lead section. I think the intelligent layman accepts that they may not be able to understand all the mathematical and physics jargon in the whole article, but they quite rightly want an introduction that can give them some intuitive notion of what QFT is about and why it might be important. In that spirit, I rewritten and have tried to simplify the lead. --Mark viking (talk) 21:48, 7 April 2013 (UTC)[reply]

Looks good to me, there's only so much you can rewrite (I still stand by an "intro" article though - to "absorb" much of the laymen description allowing this article to be as detailed as it needs to be). Anyway thank you! M∧Ŝc²ħεИ_τlk 21:56, 7 April 2013 (UTC)[reply]

Thanks, I'm glad it looks OK. I agree that an intro to QFT article would be a very good thing. The lead for the article is still quite dense in jargon and there are no illustrations to help guide intuition. These and other pedagogical weaknesses could be better addressed in a separate article. --Mark viking (talk) 23:22, 7 April 2013 (UTC)[reply]

I think this article could still be improved a lot and a separate intro article would split improvement efforts unnecessarily. This article should be an introduction to QFT, and it should be expanded on in other articles. But by all means, write a draft article if you have an idea of how it should look, then we can evaluate it, either see it is a good idea to have one, or get ideas how to improve this article. Count Truthstein (talk) 19:03, 9 April 2013 (UTC)[reply]

I know QED, QCD and beyond are relativistic theories. What are non-relativistic theories? (maybe there is none!). -- Taku (talk) 00:35, 5 May 2013 (UTC)[reply]

Most quantum field theories in condensed matter physics are non-relativistic, for example,

topological quantum field theories that don't use Lorentz symmetry. --Mark viking (talk) 02:29, 5 May 2013 (UTC)[reply

]

Ah, I see. I didn't think about these application. Thanks for the answer. I have a closely related question. I have essentially no physics background, so this is pretty basic: What is the "real" difference between QFT and relativistic quantum mechanics? -- Taku (talk) 14:02, 7 May 2013 (UTC)[reply]

Relativistic quantum mechanics (RQM) is the quantum mechanics of particles described by multicomponent spinor wavefunctions, incorporating special relativity, still using the operator formalism. Quantum field theory (QFT) has a different standpoint: particles are treated as fields, and the fields themselves are operators.

(I'm not thoroughly knowledgeable/experienced in these subjects yet, but those are the basic points). M∧Ŝc²ħεИ_τlk 14:20, 7 May 2013 (UTC)[reply]

This is a rough generalization, but...from a physical point of view, quantum mechanics describes systems with a fixed number of particles and quantum field theory describes systems in which particles may be created and destroyed, leading to a variable number of particles. Mathematically, quantum mechanical systems have a finite number of degrees of freedom, so that a wave function depends on a finite number of variables. In quantum field theory, the field has an infinite number of degrees of freedom that can represent an arbitrarily large number of particles. So the finite QM case describes dynamics with, e.g., wave functions satisfying differential equations, whereas QFT leads to fields satisfying functional differential equations. Infinite DOF in a potentially compact space leads to all sorts of interesting divergences in particle physics. QFTs in condensed matter physics come from collective excitations of a very large, but not infinite, number of particles, so such divergences are not a problem there. --Mark viking (talk) 17:03, 7 May 2013 (UTC)[reply]

Starting from this edit, to this edit and revert, followed by another revert by an IP. I think the sections should just be removed since they contain details which can just be linked to, but others are welcome to disagree. I fixed the misguided typography because it stuck out too much. M∧Ŝc²ħεИ_τlk 18:49, 14 May 2013 (UTC)[reply]

I agree that these new sections are mostly irrelevant to quantum field theory. While physics has had a long development and one can assert a rough hierarchy of dependencies (as shown by your recent illustration), not every physics article needs to cover in detail all previous physics fields that might have bearing on the topic. At most a sentence or two in the history section with wiki links to the various fields seems appropriate. I'll also note that the editor inserting these sections is very new and has also been messing with the physics templates. --Mark viking (talk) 19:27, 14 May 2013 (UTC)[reply]

Yes. Let's see if there is a third opinion. M∧Ŝc²ħεИ_τlk 19:58, 14 May 2013 (UTC)[reply]

I removed them, it's been a couple of weeks. There are complaints below as well. M∧Ŝc²ħεИ_τlk 07:40, 27 May 2013 (UTC)[reply]

From the second sentence in this section, "....came a dilemma: either preserved classical mechanics and abandoned to the rising electromagnetism, and this was preserved and abandoned almost three centuries of predictions solidly confirmed by experimentation " I tried to figure out how to make it read better, but am lost as to what the author was trying to convey. Kclongstocking (talk) 03:33, 21 May 2013 (UTC)[reply]

Sorry to butt in just like this without trying to amend the article myself but I'm in kind of a hurry (studying for some Physics exams, you know). Just wanted to point out the awful English some sections of the article are written in - almost every second sentence from "Mechanics, Electromagnetism and Relativity" onwards turns out to be barely comprehensible at all! I'd like to take the time to try and rewrite the bad parts myself, but if I am to be the one who does the job you guys will have to wait a while, I'm sorry about it...have a nice day, everyone! — Preceding unsigned comment added by Marteninthewind (talk • contribs) 15:32, 26 May 2013 (UTC)[reply]

This topic is a tricky topic, but just because the ideas are difficult is not a reason for the writing to be bad. Actually the difficulty of the topic makes it that much MORE important to write well (so the layman can try to learn something).

1. The intro sentence is too long.

"In theoretical physics, quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics, by treating a particle as an excited state of an underlying physical field."

41 words is too much for almost ANY sentence, but even more so when the topic itself is hard. The problem is the human mind has a hard time remembering of all the different sub-ideas as the sentence "runs on". Don't feel like you have to construct an entire classification style definition in the first sentence. And for a topic like this, trying to start with the analytical definition first is probably not most helpful in easing us into the topic. Instead tell us what subjects it is part of (first) or when it was developed or its importance or the like. (give us some "so what" and basic orientational ideas first, before wading into the lemma-like definitions.)

2. There is a lot of repetition:

"in theoretical physics"..."is a theoretical framework".

"quantum field theory"..."quantum mechanical"

3. The cleanup tag is very offputting to readers coming here. In addition to a tricky topic, poorly written, we get one of those discouraging, ugly templates staring at us (should be in the Talk page).

4. If the Intro is too long, consider to have the lead be very small...and then have a section itself within the article that is called overview or intro or something.

5. Too many equations in the article body. Find a way to move them to the back into a penalty box or make a spinout for THE TECHIE article, but let the main article be accessible. Certainly accessible at the front.

I know it's hard. I know there may not be a perfect solution. But there's not a doubt in my mind that this thing could not be very significantly improved and that the layman could move from getting 0-5% insights to 80% level of understanding.

TCO (talk) 20:57, 4 July 2013 (UTC)[reply]

Yes - we (at least user:Mark viking and myself) are aware of all this, it just hasn't been done yet. M∧Ŝc²ħεИ_τlk 09:41, 6 July 2013 (UTC)[reply]

I made a start at editing the history section, but even that bit needs more work. Apart from better wording and exposition, the references do not follow Wikipedia standards. I'm not in a position to do much more. — DAGwyn 71.121.204.138 (talk) 11:29, 6 February 2016 (UTC)[reply]

References all templetized and citations now uniformly in Harvard style. All for better reusability. YohanN7 (talk) 12:37, 9 February 2016 (UTC)[reply]

I am trying to add citations to the newly by User:Ami.bangali written history section. It is a lot of guesswork. Did I get Schraf 1994 reasonable right? YohanN7 (talk) 15:19, 9 February 2016 (UTC)[reply]

ψ^*(x) x ψ(x) is not the "probability density function for position." There is no such thing. This quantity is pretty much meaningless unless put under an integral, which yields the expectation value for position. --Yaush (talk) 22:00, 3 January 2015 (UTC)[reply]

I am afraid you would have to support your arguments with a reference for such a change. I'd grant you a point if the example was relativistic (though not the same point that you claim), but this example is straight-forward obvious QM. YohanN7 (talk) 23:48, 3 January 2015 (UTC)[reply]

YohanN7, it's the editor who asserts a thing who must provide citations, not the editor who challenges it. Can you cite a reliable source that speaks of probability density functions for an observable? --Yaush (talk) 23:57, 3 January 2015 (UTC)[reply]

Yes. Every QM 101 book there is. YohanN7 (talk) 01:31, 4 January 2015 (UTC)[reply]

Then it should be easy to give me volume, page, and paragraph that speaks of a probability density function for an observable. Probability density function is fine; it is, as you say, very basic quantum mechanics. It's your notion of a probability density function of a particular observable that is bovine scatology. There is no such concept in quantum mechanics.

That's what's irritating and objectionable in your repeated reverts. --Yaush (talk) 02:42, 4 January 2015 (UTC)[reply]

In the position representation, the position probability density function is given by ${\displaystyle P(x,t)=|\psi (x,t)|^{2}}$. This is equation 7.1, page 25 of Schiff's Quantum mechanics book, 3rd edition. That is, the probability that a particle is in a small interval ${\displaystyle dx}$ centered at ${\displaystyle x}$ is ${\displaystyle P(x,t)dx}$. So there is a notion of a position probability density function, but you're correct that it doesn't involve the ${\displaystyle {\hat {x}}}$ operator. If one considers mixed states, then the density matrix does provide a notion of an operator-valued probability density function, or equivalently when taking the trace with the observable, a probability density function over expectation values of the observable over the pure states. --Mark viking (talk) 06:12, 4 January 2015 (UTC)[reply]

My apologies, I read it wrong the first time around, then never really reread it. Thought you were trolling. That is, I never noticed the sandwiched operator. Yaush, I think your edit is correct. YohanN7 (talk) 13:43, 4 January 2015 (UTC)[reply]

I modified what had previously been there to the following less dramatic version:

Although the photoelectric effect and Compton scattering strongly suggest the existence of the photon, it might alternately be explained by a mere quantization of emission; more definitive evidence of the quantum nature of radiation is now taken up into modern quantum optics as in the antibunching effect.

I still think the overall impression is mistaken, though. It makes it sound like there was no evidence of the quantization of light between early experiments and "modern" experiments! Obviously the buildup of evidence over the stretch of the 20th century was massive and continuous. The extremely accurate calculations of "g" factors, for example, tended to verify the whole theory. But that is only one more glory point. Actually there are dozens of experiments and effects that could be cited. One really has to come come up with words that somehow refer to all of them.

Yet at the same time, I assume that such things as proton antibunching are part of a new, yet testable perspective, a modern window into the theory? Aren't these things tested every time people study lasers?

Perhaps the emphasis could be further shifted, by someone who knows what they're talking about. 89.217.26.179 (talk) 07:37, 28 April 2015 (UTC)[reply]

Update: there is also a citation given for the sentence highlighted in the previous comment. I omitted the citation because on a talk page, it awkwardly shows up at the bottom. But its first sentence speaks volumes (emphasis mine):

Students often believe that the photoelectric effect, and Einstein’s explanation of it, proves that light is made of photons...

89.217.26.179 (talk) 08:14, 28 April 2015 (UTC)[reply]

For what it's worth, I feel an article comparing quantum mechanics and quantum field theory is in order.

Suggest Comparison of quantum mechanics and quantum field theory. — Preceding unsigned comment added by 70.247.167.99 (talk) 13:16, 1 August 2016 (UTC)[reply]

You should probably bring this up at the physics forum where it would get more attention. YohanN7 (talk) 11:02, 11 August 2016 (UTC)[reply]

A comparison article is not entirely a bad idea, but it could introduce a lot of duplication and overlap with the main articles like

postulates of quantum mechanics... M∧Ŝc²ħεИ_τlk 14:21, 11 August 2016 (UTC)[reply

]

Should the parenthetical explanation be i.e. (as in) or e.g. (for example)?Test35965 (talk) 19:20, 10 August 2016 (UTC) Test35965 (talk) 19:20, 10 August 2016 (UTC)[reply]

A long time ago I wrote this article on the Mossbaur effect and used a simple mass-spring system to explain how the gamma rays deliver momentum to the phonon field (in a simple 1

-D model). Recently I modified that disscussion at Wikiversity:Quantum mechanics/Quantum field theory on a violin string. I would like to extend that analysis by adding an "atom" that consists of a one-dimensional simple harmonic oscillator that is weakly coupled to the phonon field. All motion is in the horizontal direction, and the coupling is the simple energy stored in a spring, ${\displaystyle {\tfrac {1}{2}}\kappa (x-\xi _{0})^{2}}$, where ${\displaystyle x}$ and ${\displaystyle \xi _{0}}$ are the displacements of the atom and central mass, respectively. Has this been done anywhere?--Guy vandegrift (talk) 07:01, 28 August 2016 (UTC)[reply]

correct words: canonical, focuses

I didn't correct them. Please do it!

User:Hullaballoo Wolfowitz removed Ken Wilson's portrait indicating it "fails NFCC#8", namely "Contextual significance. Non-free content is used only if its presence would significantly increase readers' understanding of the article topic, and its omission would be detrimental to that understanding."

This type of peremptory removal has been perpetrated repeatedly in Renormalization group as well. Omission of KGW's portrait is incontrovertibly detrimental to the readers' understanding: The article fleshes out the history of the triumphant field in the last quarter of the previous century, and, rightly, displays portraits of its creators, with explanations of their exceptional significance. KGW is, of course, king of the hill, and omitting him (for an odd technical reason ) is downright misleading, conveying the unwarranted perception that he might, somehow, be a secondary "also see". Not so, of course: KGW is all but the "owner", making magisterial sense out of the whole field. His Nobel Prize is one of the most deserving on that "wall of fame". This might not be the place to argue the merits of a wall of fame (in which, e.g., Dyson might well belong), but just a protest at the peremptory exclusion of KGW's portrait on the grounds of a counterproductive technicality. A novice skimming all this would clearly get the wrong impression. Hell, I've had students puzzling over such twists and omissions of WP all the time. For shame! Cuzkatzimhut (talk) 01:44, 1 March 2017 (UTC)[reply]

This is a garden variety example of NFCC enforcement. The text this photo is used to illustrate reads simply "They involved the work of Leo Kadanoff (1966) and Michael Fisher (1973), which led to the seminal reformulation of quantum field theory by Ken Wilson in 1975". This statement is quite lucid, and a reader's comprehension of it is not enhanced by the inclusion of a picture of Wilson. The Big Bad Wolfowitz (aka Hullaballoo). Treated like dirt by many administrators since 2006. (talk) 14:47, 1 March 2017 (UTC)[reply]

You are arguing, after all.... you selectively dropped "The renormalization group as developed along Wilson's breakthrough insights relates effective field theories at a given scale to such at contiguous scales". Indeed Wilson shared his NP with these two, but his transcendent primacy is undisputed in this field, QFT. Mentioning important chemists and condensed matter theorists should not detract from the keypoint, notional textbooks in hell or not. At best, his, KGW's, primacy should be emphasized in the text, but removal of pictures should not serve as a whip to "improve your text, or else I'll make it more misleading for you!". Cuzkatzimhut (talk) 15:59, 1 March 2017 (UTC)[reply]

And how does a picture improve the reader's comprehension of that secondary reference to Wilson? Whether nonfree content should be used is not at all determined by the importance of the subject depicted. You really should review

WP:NFC and the associated WMF policy. The Big Bad Wolfowitz (aka Hullaballoo). Treated like dirt by many administrators since 2006. (talk) 17:55, 1 March 2017 (UTC)[reply

]

My point above: it invites the reader to take Wilson's game-changing contributions as a central point, rather than as a technical aside, of course. Surely, you see the point of Einstein's picture in an article on relativity, no? You are not seriously arguing that none of the portraits of this page help the reader? Would it help your runaway enforcement objectives if the hapless reader just skipped the article altogether, and walked away shrugging, in search of a more balanced source? Remember, my gambit point above argues that Wilson's absence is in itself a significant (presumably undesirable!) message. Cuzkatzimhut (talk) 18:51, 1 March 2017 (UTC)[reply]

That's all well and good, but we're talking about striking a balance, and the WMF has directed us not to strike the balance on the terms you prefer. Moreover, the picture of Wilson was the smallest and least prominently placed in the article, and wasn't even included in the article until a few months ago (although the article has existed since 2001). Your argument, it seems to me, isn't consistent with policy, practice, and the apparent local consensus. The Big Bad Wolfowitz (aka Hullaballoo). Treated like dirt by many administrators since 2006. (talk) 23:59, 1 March 2017 (UTC)[reply]

Well, it was only the last in the article, since, as you may have cared to read, he tied the package together, at last!, so to speak. I don't know how to get across to you that he "owns" it. The article got started by newbies and even now it is struggling to improve, no thanks to roadblocks such as this. The photo was the smallest because it was of poor resolution: I certainly would not object to its being sized up! In any case, I can see you are not in a mood to be convinced, so I'll let others, preferably the Cornel publicity office, or the Nobel Foundation, do due diligence and bypass/fix the problem you created. I'm out of here. Cuzkatzimhut (talk) 01:17, 2 March 2017 (UTC)[reply]

The current revision contains the following sentence.

"In fact most topics in the early development of quantum theory (the so-called old quantum theory, 1900–25) were related to the interaction of radiation and matter and thus should be treated by quantum field theoretical methods. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra and did not focus much on problems of radiation."

Taken at face value the above seems to contradict itself, since atomic spectra consist of radiation, though not the kind being referred to in the old theory, namely, black body radiation, sometimes called incandescence. I suggest that some distinction be drawn to make the comparison clearer. For example,

"In fact most topics in the early development of quantum theory (the so-called old quantum theory, 1900–25) were related to the interaction of black-body (incandescent) radiation with matter and thus should be treated by quantum field theoretical methods. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra and did not focus much on problems of non-spectral radiation."

Since I am not a physicist, and do not wish to write anything misleading, I am not making this edit myself. Dratman (talk) 19:57, 11 April 2017 (UTC)[reply]

I'm currently translating this article to Chinese Wikipedia zh:量子場論, and have noticed several problems with this article:

1. The lack of sources in almost all sections. Who wrote all this stuff in the first place?
2. Illogical sectioning -- Why is quantum gravity a "variety of approach", but axiomatic approach is its own section? "Definitions" section doesn't actually contain any real definitions of QFT concepts.
3. Disproportionate content -- The technical build-up to canonical quantisation is too lengthy for something that isn't directly in QFT (bosons and fermions in regular QM framework). "Implications" section seems a little too specific for a general discussion of the implications of QFT. The article only alludes to path integrals and Feynman diagrams, arguably the most important concepts in QFT, but doesn't even include a single Feynman diagram.

I plan to write many sections in the Chinese article from scratch, and would like to gauge (heh) the interest over here for a rewrite of many parts of the English article as well. The sections are tentatively divided as:

• History (mostly untouched)
• Principles
  • Classical and quantum fields: Using real scalar field as an example, give the Lagrangian and state Klein-Gordon equation. Write the classical field solution as an integral of normal modes.
  • Canonical quantisation: Promote normal mode coefficients to creation and annihilation operators and construct the free theory spectrum.
  • Path integral: Heuristically explain it as the continuum limit of a series of time steps. Write a path integral as a sum over an exponential of the action.
  • Two-point correlation function: State the general formulae for the two-point correlation function in the interacting theory, using both the canonical quantisation and path integral formalisms. Mention Wick's theorem and give the Feynman propagator for the real scalar field.
  • Feynman diagram: Give one example of the use of Feynman rules in the phi-4 theory.
  • Renormalisation: Copy parts of the current "Renormalisation" section. Mention different types of regularisation schemes.
  • Other theories: Briefly discuss theories other than real scalar field with phi-4 interaction, such as QED. Write a couple Lagrangians and maybe mention the changes to Feynman rules.
    • Gauge symmetry: Introduce gauge symmetry and Noether's theorem. Copy parts of the current "Gauge freedom" section. Mention the Faddeev-Popov gauge-fixing procedure and ghosts.
    • Supersymmetry: Copy parts of the current "Supersymmetry" section.
    • (Maybe) Quantum gravity, string theory, topological QFT
• Achievements (new section): State the many achievements of QFT, such as the anomalous magnetic dipole moment, the asymptotic freedom of QCD, and the prediction of the Higgs field.
• Axiomatic approaches: (mostly untouched)

The "Principles" sections are already under way at zh:User:Yinweichen/Testpage3. Please let me know if this would be a welcome change here on enwiki. I'm also open to suggestions on further improvements (please add condensed matter content!). Cheers. Yinweichen (talk) 08:59, 9 July 2018 (UTC)[reply]

I've finished rewriting the article from scratch on zhwiki: zh:量子場論, this time with ample references. When I have the time I will translate the article to English and replace much of the current content. If there is no objection here, I'll see this as an implicit community approval of drastically changing the current article. Yinweichen (talk) 08:34, 18 July 2018 (UTC)[reply]

I've gone ahead and rewritten the English article as well, currently at User:Yinweichen/sandbox. It will be moved over here to completely replace the current article after formatting, given that there is no objection. Yinweichen (talk) 22:49, 20 September 2018 (UTC)[reply]

From a non-expert point of view I think your new version of the article is a great improvement. In the early days of Wikipedia it was felt that references were not needed in science articles for material available in textbooks or otherwise well-known. Someone would start an article and others would add to it, so organization was not a strong point. It was problems with people putting their own theories into physics articles that started the movement toward providing reliable sources. StarryGrandma (talk) 17:33, 24 September 2018 (UTC)[reply]

Almost the entire "History" section, from "Early development" to "The golden age: gauge theory and the standard model", seems to be copied from Stanford Encyclopaedia of Philosophy's entry. See this revision.Yinweichen (talk) 07:41, 11 July 2018 (UTC)[reply]

Thanks for noticing this. It was copied in Feb 3, 2016. I've removed it and requested the material be deleted from the article history. StarryGrandma (talk) 17:06, 24 September 2018 (UTC)[reply]

Please check the revision history carefully before concluding that we plagiarized another encyclopedia. I have seen a case where the plagiarism went the other way. Some jokes in the axiom of choice#Quotes article were alleged to have been taken from a certain book. But I found that those quotes were in our article even before the book was published. JRSpriggs (talk) 02:05, 25 September 2018 (UTC)[reply]

JRSpriggs, I agree that copying needs to be checked carefully, especially with all the books on Google books that are compilations of Wikipedia articles from varying dates. However the Stanford Encyclopedia of Philosophy article (written by an expert and peer reviewed) is copyright 2012, and verified at the Internet Archive. The content was copied on Feb 3, 2016 in one edit by a now blocked user. StarryGrandma (talk) 02:40, 25 September 2018 (UTC)[reply]

To StarryGrandma: Thank you for easing my mind on that. It is a shame that we cannot just block that one section, but have to block the old revisions entirely. JRSpriggs (talk) 02:45, 25 September 2018 (UTC)[reply]

It really is sad that two and a half years of history are affected. I wish we had seen this sooner. It seems the topic is so complicated few people watch it in detail. StarryGrandma (talk) 03:57, 25 September 2018 (UTC)[reply]

Thanks for looking into this. While it is sad that we have to revert so much content, a new article has already been written from scratch to hopefully replace and even improve upon the original content. Yinweichen (talk) 21:40, 25 September 2018 (UTC)[reply]

6-dimensional

All of the 10-dimensional superstring theories are still 1+1 QFTs. The QFTs of these string theories treat the coordinates of the embedding of a string into its ambient 10-dimensional spacetime as 1+1 dimensional quantum fields. In that sense, the Calabi-Yau manifolds arise in the choice of ambient spacetime on which to define the domain of these "coordinate quantum fields" living on 1+1 dimensional strings. Yinweichen (talk) 22:18, 20 May 2022 (UTC)[reply]

Here are a couple statements that look inaccurate:

Any quantum state of a single harmonic oscillator can be obtained from ${\displaystyle |0\rangle }$ by successively applying the creation operator ${\displaystyle {\hat {a}}^{\dagger }}$:

${\displaystyle |n\rangle =({\hat {a}}^{\dagger })^{n}|0\rangle .}$

Any quantum state of the field can be obtained from ${\displaystyle |0\rangle }$ by successively applying creation operators ${\displaystyle {\hat {a}}_{\mathbf {p} }^{\dagger }}$, e.g.

${\displaystyle ({\hat {a}}_{\mathbf {p} _{3}}^{\dagger })^{3}{\hat {a}}_{\mathbf {p} _{2}}^{\dagger }({\hat {a}}_{\mathbf {p} _{1}}^{\dagger })^{2}|0\rangle .}$

What about superposition states (such as coherent states)? For a harmonic oscillator, only energy eigenstates can be obtained by successively applying the creation operator to the vacuum.76.176.180.164 (talk) 18:51, 30 June 2020 (UTC)[reply]

This has been clarified. Thank you. Yinweichen (talk) 22:22, 20 May 2022 (UTC)[reply]

An article on QFT without a definition of what a quantum field is? An article written by another academic who lost sight of reality? — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 21:50, 29 October 2020 (UTC)[reply]

Defined in section 2.2 through illustration. It is made evident before that it is a quantization of a classical field.Cuzkatzimhut (talk) 03:00, 30 October 2020 (UTC)[reply]

Perhaps Wikipedia deserves an Introduction to quantum field theory, something similar to Introduction to general relativity that is more less technical and more approachable to laypeople. Yinweichen (talk) 22:24, 20 May 2022 (UTC)[reply]

There is discussion in talk:Higgs boson about Higgs boson (particle) vs. Higgs field, up to renaming the article. It occurs to me that many, especially those who know just enough physics to get confused, have a hard time understanding that quantum particle and quantum field are just two different ways to look at the same thing. In everyday life, we don't get confused over what is a particle and what isn't. In any case, I wonder if this article should discuss particle vs. field, or if there should be a separate article to do it. Gah4 (talk) 20:29, 7 January 2022 (UTC)[reply]

The article does phrase it quite explicitly that "QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles." It also describes the historical development of the wave-particle duality in the History section, leading up to the understanding that each type of particle has its own corresponding quantum field, and the interactions are described as between fields. What would you propose to add to the article to make it more readable to laymen? Yinweichen (talk) 22:10, 20 May 2022 (UTC)[reply]

It isn't that it especially bothers me. I suspect I don't understand QFT quite as well as I could, but enough that I don't have a hard time thinking about both particles and fields. But many people only know it about as well as they teach in 5th grade. That light is either/both a particle and wave, and then leave it at that. As well as I know it, about the time that Einstein was talking about photons, Planck still didn't believe in the quantization of the EM field, and might never have. Maxwell's equations worked so well, that it was hard to explain why they were wrong. Thinking about it now, it is interesting that spin 1 particles have the properties of vectors, where other spin values don't. Some might want to read about the Higgs boson, without needing to understand this article. It isn't so much of a problem for photons, a little harder for electrons, but I suspect a lot harder for Higgs. Gah4 (talk) 00:21, 21 May 2022 (UTC)[reply]

If one has a quantum mechanics training (as in, they know about raising operators and the ground state), then they can understand what QFT calls "a particle" from the canonical quantisation section. If one doesn't, then I'm afraid the simplest explanation is through analogy. Whatever it means for light to be both a field/wave and a particle, that's exactly what it means for an electron, proton, or Higgs boson to be both a field/wave and a particle. Yinweichen (talk) 04:03, 21 May 2022 (UTC)[reply]

In the case of Higgs, or any particle in the news for being detected, it is nice for people to know what it means to "detect a particle", such as in the LHC. Or as it might be explained in 5th grade, to detect a photon. In explaining that a Higgs was detected by the LHC, raising operators don't really help much. I suppose it does when discussing lifetime, but that seems rare in popular discussion about Higgs. The question months ago came from discussion about renaming the Higgs article to

Higgs field or something similar. Gah4 (talk) 18:19, 21 May 2022 (UTC)[reply

]

I understand what you mean now. In short, the LHC detected the decay of individual Higgs bosons, created out of the Higgs boson field, which permeates all of space at all times. In that sense, it is the particle that was observed directly (or really indirectly via its decay products), and from the detection of this particle, we can conclude that the Higgs field is real. One could say that one cannot detect a calm lake but can only detect ripples and splashes from the pond. In this analogy, the pond is the field, and ripples and splashes are the particles. If there is a good source that discusses this concisely, it would be a good addition to the article. Yinweichen (talk) 07:38, 22 May 2022 (UTC)[reply]

"QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles."

So as others have suggested, this article needs a particle vs. the underlying reality statement. If this theory proves correct, then what we call particles are more precisely quantum field fluctuations. It is believed (Leonard Susskind Stanford lecture) that there are multiple quantum fields which create the phenomena that have been described as quantum particles. Particles are random fluctuations in quantum field energy levels.~~ The age of fable (talk) 17:08, 28 September 2022 (UTC)[reply]

I watched some Susskind lectures, but more Feynman lectures. He has one where he compares bullets (discrete, no interference), water waves (continuous, interference), and photons (discrete interference). Also reminds me that Planck did not, as well as I know, ever believe in the quantization of the EM field. That is, emission and absorption were discrete, but the field itself was not. Partly that might be that Maxwell's equations work so well, that they couldn't be wrong. Or that it was a mathematical trick that got the right answer, but wasn't actually real. In any case, yes it is hard to visualize quantum fields. Gah4 (talk) 20:38, 28 September 2022 (UTC)[reply]

This page is not a forum for general discussion about Quantum field theory. Any such comments may be removed or refactored. Please limit discussion to improvement of this article. You may wish to ask factual questions about Quantum field theory at the Reference desk.

The section above was meant to help understand QFT in the case of Higgs boson, and especially to make it more understandable by non-experts. Specifically, the question of particle vs. field. It is meant to improve either this article or Higgs boson, or both. Since it is not easy to understand, it is not surprising that discussions on improving it are not easy to figure out, though I was not expecting {{not a forum}}. Gah4 (talk) 09:54, 29 September 2022 (UTC)[reply]

It is stated early in this topic that the Standard Model was "completed" in the "1970's". I just finished watching a talk by Feynman on the subject of the Strong Force given in 1977. It's pretty clear that the Standard Model wasn't yet complete. Only 4 of the eventual 6 quarks had been discovered and the charm and strange quarks were not known to be on the same hierarchy level. The J/Psi particle had been described, but the were at least two other Weak Force particles yet to be discovered. The Higgs was not confirmed until 2012. Dwinsemius (talk) 00:56, 22 September 2023 (UTC)[reply]

The SM was Conceptually complete by 1980, indeed. No serious researcher had any qualms, or doubted the unobserved particles would be there. Not even neutrino masses disrupted this picture. I was assisting Feynman at the time and he had no misgivings or doubts. Unscrupulous popular science journalist have been playing up unwarranted doubts for 40 years since, since they fail to understand the real tight logical structure involved. The third generation was guaranteed to be there by anomaly cancellation and clinched by the discovery of the b quark. Hedging the date given would be quite misleading. Cuzkatzimhut (talk) 12:18, 22 September 2023 (UTC)[reply]

Do you have any citations? Let me offer another citation: the Nobel lecture of Marting Perl, given for the discovery of the tau lepton. On page 187 he says there was serious resistance to the notion that there was a third generation of particle. He also writes that there was general acceptance of two generations of quarks and leptons, which included the charm particle but no mention of top or bottom quarks. Dwinsemius (talk) 20:34, 22 September 2023 (UTC)[reply]

Let me apologize for misspelling Martin Perl's first name. And let me offer another reference to a Nobel Prize lecture, this time from Sheldon Glashow in 1979 and with text:

"The discovery of the in 1974 made it possible to believe in a system involving just four quarks and four leptons. Very quickly after this a third charged lepton (the tau) was discovered, and evidence appeared for a third Q= -1/3 quark (the b quark). Both discoveries were classic surprises. It became immediately fashionable to put the known fermions into families or generations: The existence of a third Q = 2/3 quark (the t quark) is predicted. The Cabibbo-GIM scheme is extended to a system of six quarks. The three family system is the basis to a vast and daring theoretical endeavor. For example, a variety of papers have been written putting experimental constraints on the four parameters which replace the Cabibbo angle in a 502 Physics 1979 six quark system. The detailed manner of decay of particles containing a single b quark has been worked out. All that is wanting is experimental confirmation. A new orthodoxy has emerged, one for which there is little evidence, and one in which I have little faith. The predicted t quark has not been found. While the upsilon mass is less than 10 GeV, the analogous tt particle, if it exists at all, must be heavier than 30 GeV. Perhaps it doesn’t exist."

So I think it would be accurate to say that the components of what became the Standard Model were available, but that it could not be considered "complete" until somewhat later than "the 1970's". Dwinsemius (talk) 21:20, 22 September 2023 (UTC)[reply]