Talk:Quantum field theory

What is "a QFT"?

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)

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)

Citation needed

The non-existence of a wave function for a single photon is described here . 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)

References

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

Constructive and axiomatic QFT articles

(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)

Fucking useless

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)

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)

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)

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)

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

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

Thoughts on article

There are some points that the article doesn't make clear.

The main thing is to define what the states are and what the operators are which act on this state (representing observables or otherwise). Would I be right in saying that all states can be build out of the vacuum state "|0>" by applying (sums, multiples, products or integrals of) creation or annihilation operators? To what extent are these expressions formal, i.e. not to be evaluated? (Normal ordering should be mentioned here.) What are the observables and what are the corresponding eigenvectors and eigenvalues? What states correspond to, for example, particles with a definite momentum or position? If the state (the ket vector in Hilbert space) is an element of Fock space, then surely you can't really say that the quantum field should be thought of as permeating space and time with a value at each point (e.g. for spin-1/2 fermions, it's supposed to be a spinor field), as an element of Fock space isn't a function of position? But the Lagrangian density is still defined in terms of position and is used to describe the field's dynamics, so where does that fit in?

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

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)

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 Standard_Model_(mathematical_formulation) does a better job at showing examples - maybe this article could briefly summarize types of field (vector, scalar, spinor) with examples of Lagrangians, observable states etc. for each. The description of the occupancy number representation in the article is slightly confusing as it assumes that the number of states is countable, so this would have to be tweaked when examples are covered where this is not the case. Count Truthstein (talk) 18:39, 29 December 2012 (UTC)

New article: Introduction to quantum field theory?

Concerning the "f*@!#~? useless" comments above, would a new article help? C.F. Introduction to angular momentum, Introduction to general relativity, Introduction to quantum mechanics, probably others... I raised this point here also. Thanks, M∧Ŝc²ħεИ_τlk 15:22, 7 April 2013 (UTC)

Rewrote lead

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)

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)

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)

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)

Is there such a thing as non-relativistic QFT?

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)

Most quantum field theories in condensed matter physics are non-relativistic, for example, phonons. If there is a quasiparticle, there is generally a QFT behind it. Euclidean field theory used in statistical physics is non-relativistic. And I would have to look it up, but I think there are some formal topological quantum field theories that don't use Lorentz symmetry. --Mark viking (talk) 02:29, 5 May 2013 (UTC)

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)

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)

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)

New interrupting sections?

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)

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)

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

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)

Under the section "Mechanics, Electromagnetism and Relativity"

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)

Bad English here

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)

this article could be better written

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)

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)

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)

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

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)

Confusion about probability density function

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)

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)

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)

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

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)

In the position representation, the position probability density function is given by $P(x,t)=|\psi (x,t)|^{2}$. 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 $dx$ centered at $x$ is $P(x,t)dx$. So there is a notion of a position probability density function, but you're correct that it doesn't involve the ${\hat {x}}$ 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)

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)

Emphasis in a sentence about early versus recent evidence

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)

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)

Comparison

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.