What can be called a fundamental theory?

[Phiphy]

The usual perception is quantum field theory is not fundamental since it has divergence. A fundamental theory must always be finite, like string theory.

But in the physical sense, a fundamental theory means it is valid at any arbitrary energy scale. We know that non-renormalizable theories are not fundamental because they must break down at a finite cut-off; QED is not fundamental because it blows up at the Landau pole. However, QCD is asymptotically free and I see nowhere it must break down. Suppose we have only QCD in our world. There is no EW theory or gravity. do we still worry about the divergence in QCD and set off looking for a fundamental mother theory for QCD? In other words, is divergence really physical so that we must find something to cure it?

 

[humanino]

QED is not fundamental because it blows up at the Landau pole.

I would typically consider this example to be an academic problem showing unreasonable conditions for a "fundamental theory". The landau pole is even above the Planck scale. We have quite a different perspective on renormalization since Landau came up with this pole.

 

[hamster143]

As long as it requires renormalization, it's not fundamental.

 

[humanino]

As long as it requires renormalization, it's not fundamental.

If anyone tries to sell you a field theory claiming that it holds up to arbitrarily high energies, you should check to see if he sold used cars for a living. (As I wrote this, a colleague who is an editor of PRL told me that he worked as a garbage collector during high school vacations, adding jokingly that this experience prepared him well for his present position.)

The book was written in 2003. Landau died in 1968.

 

[Phiphy]

The book was written in 2003. Landau died in 1968.

Thank you for mentioning A Zee. It was exactly what he said in his book(QFT in a Nutshell) made me bring up this question. I still don't understand why this "divergence" criterion is reasonable.

Let's put it in this way. I remember Zee also said in his book, "theories in physics have the ability to announce their own eventual failure and hence their domains of validity". So even if we put aside all the divergence or renormalization criterions, we can ask one question: Is there any where that QCD cries out its failure by its own? There are several possible answers:

1 QCD can be fundamental in principle so it cannot show its domain of validity by itself. Only conflicting with other theories (Eg. gravity) can bring it down.

2 QCD cannot show its domain of validity because it's not a good physical theory. We can get a reasonable result (finite, respecting unitary, perturbative, etc. ) at an arbitrarily high energy, however it conflicts with experiments. (Even worse than a EFT in this sense.)

3 QCD can show its boundary and we'll somehow see that the cut-off cannot be pushed to infinity. (However, I can't imagine how this would happen. )

4 This question is nonsense. Gravity can never be avoided in any complete fundamental theory, so we can never separate QCD or whatever "good" field theory from gravity. And gravity says, all field theories are doomed.

Which one might be the most reasonable answer?

 

[hamster143]

Since we're quoting things, here's one more quote:

I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the theory involved in this case is not that.

- Supreme Court Justice Potter Stewart, quote slightly modified

But seriously, even if we forget about renormalization and divergences within QCD itself - QCD does not incorporate gravity, and QCD has to be unified with electromagnetism, which does blow up near Landau Pole. Therefore, QCD is not fundamental.

 

[humanino]

electromagnetism, which does blow up near Landau Pole.

Did you notice that we already know something occurs with EM at the so-called electroweak scale ? There was a nice plot from ZEUS

 

[genneth]

To answer the OP: QCD alone, is mathematically elegant and as far as we know, free from UV problems. However, QCD is manifestly not sufficient. The other bits do have UV problems. It is currently not understood whether the non-QCD bits and the QCD are linked at some high energy, but it is widely thought to be so; thus any problems they have should be related.

As a condensed matter theorist I'm never going to believe any claim that a theory is UV complete. The very essence of universality is that a wide variety of theories tend to have the same low energy behaviour, and it is pure hubris if we believe our current HEP theories to be exempt --- QCD included.

 

[Phiphy]

In fact I am very glad to see that QFT must break down at some point. Maybe my question is too conceptual to get a concrete answer. Let's just leave it as it is.

A different but related question:
Can anyone remind me why gravity cannot be quantized as a field theory? Is there any simple reason? Maybe by answering this question can we understand why QFT is not fundamental.

 

[humanino]

Since I have too little strength to answer seriously to this thread, I'd like to post a link to a paper by Weinberg which is more than 10 years old and tells it much better than I can.

http://xxx.lanl.gov/pdf/hep-th/9702027v1

Note that GR is not renormalizable from a power counting point of view only.

 

[Phiphy]

Thank you, Humanino.
I read this paper one year ago, however I did not fully understand it. Think I should read it again.

 

[humanino]

I'm note exactly sure what you are trying to nail down, whether it is about QFT or renormalization. The above paper by Weinberg sums up rather well what seems to me is the modern point of view on QFT. For renormalization, there is a very good introductory paper which does not depend on QFT by itself :
A hint of renormalization

An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what is specific to field theory and what is intrinsic to renormalization. We link the general arguments and results to real phenomena encountered in particle physics and statistical mechanics.

 

[humanino]

See my thread in the Independent Research section.

It is innapropriate of you to quote the Independent Research forum here.
Please provide a published reference to your work.

 

[humanino]

The works were published long ago, in the USSR.

I hear a lot of that. Well, sorry but I'll be frank with you : if your work had any value, you would not have any difficulty to publish it in English for everybody to read and it should be your DUTY to publish it in English so that it does not fall in forgetfulness. Besides, I do not believe it is common practice on PF to accept foreign language publications, for obvious reasons.

Please take into account that it is already too difficult to read what is published, so please do not expect people to pay attention to things not published, such as "I posted it on arXiv".

 

[Bob_for_short]

...I'll be frank with you : if your work had any value, you would not have any difficulty to publish it in English for everybody to read and it should be your DUTY to publish it in English so that it does not fall in forgetfulness.

They were translated into English but are not available on internet (too old publications).

Besides, I do not believe it is common practice on PF to accept foreign language publications, for obvious reasons.

Do you think the Russian science is wrong or different?

Please take into account that it is already too difficult to read what is published, so please do not expect people to pay attention to things not published, such as "I posted it on arXiv".

Your reference to "Renormalization hint" points out to arXiv. The article is written by a french researcher, like me. You are too hostile to me personally.
What I do is answering questions that persist despite a huge amount of mainstream answers.
I have a unique and helpful experience in solving problems. You even cannot imagine to what extent you are unjust to my efforts.

P.S. I removed my answers from this thread.

 

[humanino]

Do you think the Russian science is wrong or different?

Yes I think it is different, and I have a lot of respect for the Russian school, as a matter of fact my best teachers were Russians.

You even cannot imagine to what extent you are unjust to my efforts.

Then do not be unjust to your own efforts, and publish them in English ! Seriously, I am quite interested by the renormalization procedures, and although I am not researching professionally I try to read as much as I can.

 

[Bob_for_short]

Yes I think it is different, and I have a lot of respect for the Russian school, as a matter of fact my best teachers were Russians.Then do not be unjust to your own efforts, and publish them in English ! Seriously, I am quite interested by the renormalization procedures, and although I am not researching professionally I try to read as much as I can.

As soon as it's been published already in western journals (and present at some libraries) I prefer to submit English translations to arXiv and refer to the journal versions in the Literature chapters.

 

[Bob_for_short]

...Seriously, I am quite interested by the renormalization procedures, and although I am not researching professionally I try to read as much as I can.

"Reformulation instead of Renormalizations" is even simpler and more relevant than "A hint of renormalization". It's also been written with pedagogical purposes and contains an explanation of the anatomy of renormalizations.

 

[ZapperZ]

This thread has gone seriously off-topic, so I assume that there's nothing more to be discussed with respect to the original topic.

Zz.