Talk:Quantum field theory

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I think someone got the formula for the symmetric wave-function of a system of N bosons wrong. As it stands, it is not correctly normalized. What's really funny is that later on we have a (correct) example for a system of three particles which is not consistent with the general formula.

Well, I'd personally prefer a treatment of relativistic QFT expressed in the language of physics rather than mathematics. But I don't have time to work on the article right now. Oh well. -- CYD

I think something needs to be said about what is quantized. In QM we quantize the [x,p], but in QFT x,p are not really operators, instead we quantize [field,canonical momentum] which are operators. (and the field is not an operator in regular QM).

Also I think something needs to be said about the propigator greens function that really captures the heart of partical exchange and lots of new ideas. -- CHF

"What is quantized?" is a deep question. There should be a discussion of relativistic canonical quantization.

I'm unclear on what the complaint above is about. Given that this is about quantum field theory, what makes the article too focused on quantization? -- KarlHallowell 16:23, 1 November 2006 (UTC)

Contents

[edit] simplify!!!

Could we either make a Simple English version of this article or explain it in terms that someone other than a physics major might understand? I consider myself to be fairly intelligent, fairly knowledgeable in physics and at least slightly knowledgeable in quantum mechanics (I've watched What the Bleep 3 or 4 times), and yet I have been unable to understand most of the articles regarding quantum theory in Wikipedia. Particularly the summary at the beginning of the article should use as few technical terms as possible and provide a clear, simple idea of whatever the article is about. Lord mortekai (talk) 05:31, 20 December 2007 (UTC)

[edit] tex in text

Recently, 145.254.153.97 changed a whole bunch of inline math from html tokens to <math> markup, whereas my understanding is that the preferred standard is to use html tokens for inline text, and the <math> tags for display mode formulas. Perhaps there is some reason that this article should break with this standard? -Lethe | Talk

It isn't really my area, but the schrodinger equation as quoted looks suspicious to me. Specifically, is it correct to have |p|^2 *\del ?

The Schrodinger equation is correct. p is the momentum operator. -- CYD

[edit] Reorganization and request for collaboration

I started fiddling with this page and its turned into a major reorganization. Sorry if I stepped on some toes. Let me explain. I've added a history section at the top (which could link to an article on QFT history if someone is willing to write it). Canonical quantization should have its own page (I started it recently): but some people have worked hard here on the second quantization sections, which should be merged there. I don't want to do this without first putting my intentions on this page and listening to other ideas. The way I think right now is that it would be good to talk about canonical and path integral methods in general here, and then refer to quantization (physics) for more.

What of this page then? What should it contain. It should expand into the 50's and 60's through gauge theory, and go on to give an overview of QFT today, which includes condensed matter physics and particle physics and the essential use made of the renormalization group and statistical field theory (how can that be in red!). It should also talk about connections with string theory. And it should do all this without being overcome by details, because they can be relegated to each of the topics separately.

Tall order, I know. I'm asking you for help: for ideas, help on new articles and wiki expertise. Bambaiah 10:49, Jun 6, 2005 (UTC)

Firstly, canonical quantization isn't the same as second quantization. The former is a recipe for going from a classical field theory to a quantum field theory; the latter is a recipe for going from a single-particle quantum theory to a quantum field theory.
You could treat it as such, but a modern text book (see Weinberg vol 1) doesn't make this distinction. Bambaiah 13:33, Jun 20, 2005 (UTC)
Also, in the maths field,I've seen certain h-based deformations of algebraic classical systems refered to as second quantization. Ie, it's very close to canonical quantization, but viewed from the perspective of deformation theory. KarlHallowell 16:50, 23 August 2005 (UTC)
The discussion of second quantization was written by me. I wanted to provide a demonstration of the essential features of quantum field theory is, at a level that anyone familiar with quantum mechanics can grasp -- e.g.,
  • The fact that quantum field theory is a subset of quantum mechanics
  • The essential role played by particle creation and annihilation
  • How particle indistinguishability is "automatically" handled
  • The physical meaning of the field operator (which is not always so clear if you proceed from canonical quantization)
Still, perhaps the discussion goes into too much detail, at the expense of the other approaches. In particular, I do agree that a discussion of the path integral approach is sorely lacking. But I think that, in any rewrite of the article, the above points have to be retained. As for gauge theory, renormalization, and string theory, my feeling is that these are too specialized for an article on "quantum field theory" in its most general sense. There are plenty of useful quantum field theories thare aren't gauge theories, nor renormalizable, nor have any bearing on string theory. These topics deserve a brief mention at the end, at most.
The part on second quantization is nicely written. QFT⊂QM should clearly be emphasized, as should the essential conceptual role of single particle excitations. I think of your contribution to this article as valuable, that's why I opened this dialogue. I guess we agree then that an overview article should
  • explain the scope of the subject,
  • describe the main applications,
  • outline the inter-relations between the parts,
  • point to detailed articles on everything covered.
The word general that you use is inclusive; that is exactly the sense in which I see this article. Bambaiah 13:33, Jun 20, 2005 (UTC)
Finally, the "History" section should be at the end of the article. I think it's more logical to explain what quantum field theory is first, and then talk about how people worked it out; not the other way round. -- CYD

I have no problem with that; in fact, I think the main history should be moved out into a different article. I'm following up on that right now. Bambaiah 13:33, Jun 20, 2005 (UTC)

The fact that quantum field theory is a subset of quantum mechanics
In what sense do you mean this? I would have said it's quite the other way around. Quantum mechanics is a special case of QFT (QM is QFT in 0+1 dimensions. or, alternatively, QM is the dynamics in the single particle Hilbert subspace of the QFT Fock space. Either way of looking at it, QFT is a superset of QM.) -Lethe | Talk 21:04, Jun 7, 2005 (UTC)
Simple. All quantum field theories are quantum mechanical; but not all quantum mechanical theories are quantum field theories. QFT is simple an application of the postulates of quantum mechanics to fields. -- CYD
But every QM theory is a QFT. Put QFT in a 0+1 dimensional spacetime, and you have QM... so ... ? -Lethe | Talk 10:35, Jun 8, 2005 (UTC)
By your definition, the theory of a single spin-1/2 system is also a QFT. That's rather a stretch, since there is no field in the theory at all. -- CYD
the intro should give a quick explanation of what a QFT is, the history section should explain why it is; what _problem_ it attempts to solve, IMHO --MarSch 12:48, 8 Jun 2005 (UTC)
on second thought (and a better look at the article), I support moving the history to the end or down in any case. There is already a section specifically devoted to _why_, which (existence) I think is great. --MarSch 12:50, 8 Jun 2005 (UTC)
Done. Bambaiah 13:33, Jun 20, 2005 (UTC)

Reworked the first paragraph of the "Why" section. Originally, I wanted to remove "necessitated" from the picture, but there was a slippery slope. BTW, I seem to recall that this work was on electrons not atoms. One of Dirac's key discoveries here was the existence of the positron which came a bit later. I think that was when spinors entered the picture for QFT too.

[edit] Problem with normal modes

For the definition of normal modes, you refer a text which uses sine waves which have no physical meaning because it would be infinite in time. Planck had not this problem because he introduced a bandwidth.

Maybe the solution would be the use of the mathematical definition of the modes which works well in classical electrodynamics: given the linear equations of a field, a mode is a ray in the real space of the solutions of the equations. The scalar product (therefore orthogonality and norm) are deduced from a MATHEMATICAL comparison of the energies of two modes and of their sum, assuming that there is only the given fields. —Preceding unsigned comment added by JMO (talk • contribs) 16:30, 17 October 2007 (UTC)

Bandwidth doesn't get you around the problem since a sine wave has a single frequency - the narrowest bandwidth of all. There are computational advantages to using normal modes. They span the span of physical states, are eigenstates of certain derivative operators, and transform nicely under Fourier transforms (eg, between position and momentum space in Euclidean space). -- KarlHallowell 20:53, 17 October 2007 (UTC)

[edit] Confused

Can someone please reword or clear up this statement:

"Only by accident electrons were not regarded as de Broglie waves and photons governed by geometrical optics were not the dominant theory when QFT was developed."

found at the end of "Quantization of classical fields". I don't understand what this is getting at and when I read it, it seems like there is a double negative.

01:14, 6 February 2006 (UTC)

[edit] Witten?

I don't think it is appropriate that the picture of Witten appears here, while pictures of much more important figures in this context, such as Feinmann, do not. I intend to erase it. Shokopuma 20:24, 4 May 2006 (UTC)

well that would be an improvement! Why don't you find a picture of Feynman and put that up, before removing Witten. --MarSch 09:36, 5 May 2006 (UTC)

[edit] Experiments

I think there should be something about experimental support for QFT. This is physics after all... I mean QED is known to be very accurate (well, not that the QED page gives any details except the mythical number 10^-12) but how good is the experimental evidence for QFT? Maybe a link to the Casimir effect page? Anything else? —The preceding unsigned comment was added by 192.16.204.78 (talk • contribs) .

Do you realize that QED is a kind of QFT? —Keenan Pepper 19:26, 19 May 2006 (UTC)
Well as Keenan was saying, QED is a QFT which has some amazingly accurate predictions. But QFT covers a broad category of theories, some of which are so broken that they can't ever describe a physical world, much less our particular physical world. -- KarlHallowell 22:24, 21 May 2006 (UTC)
The little I remember from the course, you don't need the QFT formalism to caculate, say, atomic spectra, the most famous prediction of QED (and the one that the 10^-12 number relates to). Is that correct?
No idea here. Though as I understand it, the point is that the QED prediction is extraordinarily accurate. Not that it's the only model (or perhaps the only tools) that can make such a prediction. -- KarlHallowell 10:46, 18 June 2006 (UTC)
QM can calculate the atomic spectra but with many pertubative additions to the initial Hamiltonian used. Some of these perturbations are ad hoc, to the best of my knowledge. Most quantum books do go over a few of these additions needed. QED on the other hand, recquires none of these corrections to accurately describe the atomic spectra. I had to do this once for a homework problem long ago, it takes quite a bit of work. If i have time i will find a reference, but it would not likely be a text book. You will have to look at the original papers which are likely too old to be found online. Maybe someone scanned their work and post it online? --Blckavnger 19:50, 21 November 2006 (UTC)

[edit] Raphtee, why I undid your edits

Raphtee, here's why I undid your edits in the "Description" section. While it is true that one can trivially write any quantum mechanical system as a zero-dimensional QFT, this doesn't add any information since the QFT aspect isn't used. Ie, it has no explanatory power. To my knowledge, no one uses this fact pedagogically when teaching QFT. It's useful to know that one can do so at some point, but I see no point to have that in the wikipedia. On the other hand, knowing that a QFT is a special quantum mechanics model is very useful. That means it has an inner product, state space, and other things associated with quantum mechanics models.

You comments on tensor fields are worthwhile. I decided to rewrite that paragraph to indicate that particles with spin can be represented as tensors and as spinor-tensors, and that there are transformation rules for the resulting set of fields. This may be overly complex for this stage of the article. I'm not attached to it.

Energy states are eigenstates (also sometimes called eigenspaces, eigenvectors, eigenmodes, etc depending on the context) of the Hamiltonian not eigenvalues (which are scalars not states) which physically are the energy of the corresponding eigenstate.

Finally, I'm not sure that the comment,

(QFT appears in the continuum limit of condensed matter systems).

belongs in the Description section, but I wasn't comfortable with its removal given the other things going on.

So that's why I reverted your changes. -- KarlHallowell 02:05, 10 March 2007 (UTC)

[edit] Article's essay style

I find this article reads like an essay and just tagged it as such. The content seem all good, but the tone sounds a bit off. Examples, with some of what I find "offending" to encyclopedia style emphasized:

  • Quantum field theory corrects several limitations of ordinary quantum mechanics, which we will briefly discuss now. [here, the part after the comma sounds redundant]
  • (...) one can create a (rather successful) theory of many particles. Here is how it is:
  • We may well ask whether these are operators in the usual quantum mechanical sense, i.e. linear operators acting on an abstract Hilbert space. In fact, the answer is yes (...)
  • One may notice from this that applying a fermionic creation operator twice gives zero (...)

I think some parts are better off than others. For example, the introduction, Origin, Gauge theory, Supersymmetry, and History sections look good here. A "we" form seem to be common throughout the article, and overall it's often "wordy", and I think encyclopedic articles should concentrate on explaining the facts, not try to talk to the reader, as in giving a lecture.

I'm not going to start editing things right away because I'd like to hear input on this, and also because English is not my mother tongue, so I'd like to confirm if I'm at least on to something here, or if I'm completely off base. ;-) -- Northgrove 01:07, 15 March 2007 (UTC)

[edit] Lead sentence

"Quantum field theory (QFT) is the quantum theory of fields."

...that is pretty unhelpful. Anyone have the expertise to rewrite lead sentence without self-definition? 67.40.31.115 18:06, 22 May 2007 (UTC)


[edit] Section 3.1.1 Large number of particles

This section contains errors. Indeed, you can write the wavefunction of a many-body N-particle system as its factorization in the product of N 1-particle wavefunctions (as in the reported formula) ONLY IF the particles are non-interacting. But in that case there is no many-body problem. The problem in many-body is that you can't write simply the wavefunction even for the ground state. That's why a field theoretic treatment is required.