Talk:Quantum field theory

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.

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

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)

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)