Searching for the Higgs Field: 95% Confidence of Existence

[yquantumjumps]

Hello,

For clarification because of the ambiguous situation in searching for & concerning the Higgs Field. It is with 95% confidence that the Higgs Field exists.

Yet it has not been seen as of the end of 2005. I hope LHC/CERN will shed light on the subject. Anyone dealing or knowledge of the Higgs Field, do you expect it to be found.

Your comments would be greatly appreciated at this point in time.

Thanks,
BGE

 

[Hans de Vries]

Hello,
For clarification because of the ambiguous situation in searching for & concerning the Higgs Field. It is with 95% confidence that the Higgs Field exists.
Yet it has not been seen as of the end of 2005. I hope LHC/CERN will shed light on the subject. Anyone dealing or knowledge of the Higgs Field, do you expect it to be found.
Your comments would be greatly appreciated at this point in time.
Thanks,
BGE

The Higgs field made it possible to in 1971 to renormalize the Yang-Mills
gauge theory associated with the united electroweak force. ('t Hoofd)
It was Steven Weinberg's paper from 1967 "A model of Leptons" in which
he proposed the correct Electroweak Lagrangian. (Phys.Rev.Let vol.19
Issue.21 1264-1266 )

He mixed in Goldstone bosons which are later eliminated in the interactions
just leaving a coupling which gives rise to the masses of the intermediate
vector bosons W and Z and the leptons.

So something should be right here. The theory itself however doesn't predict
any specific mass nor does it predict the mass of the Higgs bosons.There's an interesting follow-up paper from Weinberg in 1971 after the
so important proof that it was renormalizable:

"Physical processes in a convergent theory of the Weak and Electro-
magnetic interactions" (Phys.Rev.Let vol.27 Issue.24 1688-1691 )
Regards, Hans

 

[yquantumjumps]

Higgs

Thank you Hans,

I am aware of the papers, it is greatly appreciated. [Drs. R. L. Mills & C. N. Yang / Drs. Glashow, A. Salam & Weinberg in the award pointing the way].

I am in a discussion of the GeV needed, some believe it will be
115 GeV/c^2, I believe more in the 250 GeV/c^2.

In its predictive power of the Higgs Field, you know that it would tidy up some questions in the Standard Model which is needed at this time, also provide a description of microscopic matter and the fundamental interactions - origin of all mass-. Would you not agree?

It is not taken lightly here that to discover the mechanism for mass would benefit greatly. I apologize for not making myself clear.

Thank you for your comments,
BGE

 

[Ernies]

The Higgs field made it possible to in 1971 to renormalize the Yang-Mills

so important proof that it was renormalizable:

"Physical processes in a convergent theory of the Weak and Electro-
magnetic interactions" (Phys.Rev.Let vol.27 Issue.24 1688-1691 )



Regards, Hans

Why does the concept renormalisable make things acceptable? It is no more than sweeping things under the carpet by saying infinity - infinity=0.
And at least half a dozen prominent physicists have so described it in discussion -- though no doubt in writing they would have been more circumspect. if you know of a real justification i would be glad to hear iit.

ernie

 

[yquantumjumps]

Good question.

ernie,

It is hard to read the emotion dealing with correspondence, unless you put it all in upper case. I think you are just asking why?

I am not sure this is to be proactive in the search or just frustration in what we are dealing with in the Higgs.

It is a very hot subject this you know. You mentioned renormalization, I will go three years later to 1974 by K. Wilson, when he used the tool to achieve his goal. He called it the, 'renormalization group,'

You being a mathematician I believe understand this only means, applying a new normalization or new calibration dealing with the theory and its parameters in which you are studying at the time. Example, energy.

I believe you also know symmetry & symmetry breaking that helps us all to understand how the universe we live in works, like from an undifferentiated point to the complex structure we view, so we are searching for the Higgs in order to understand how mass relates to W's & Z & still the photons remains or stay in the same state, massless.

Your question, "what is the real justification it this approach?" Is!

To answer the questions dealing with mass that has perplexed many physicist dealing with the Standard Model, we are about 95% it is there, and it fits in theory, yet it has of 2005, not been verified (you seem very knowledgeable, so I do not feel I need to expound on this).

BGE

 

[humanino]

Why does the concept renormalisable make things acceptable? It is no more than sweeping things under the carpet by saying infinity - infinity=0.

It is certainly more than just that for sure ! Renormalizability is a very important issue, and everybody agrees that it is not fully understood. But unless you pretend to have theory valid at every energy scale AND finite, you need renormalization.

Apparently Alain Connes has made quite profound progress in understanding the nature of the process of renormalization. For two reasons I cannot talk about it : it is too complicated for me (Non-commutative geometry, NCG), and it belongs to another forum.

if you know of a real justification i would be glad to hear it.

Once again I could quote NCG, but that's already unfair.

Whatever people try to do to deal with the origin of mass, a scalar field must enter into the game. People trying to introduce it directly with gravity must include a dilaton for instance. This is the same in string theory, the scalar field is the dilaton. In Gribov's scenario for confinement, the scalar field is a condensate of fermions.

Anyway, most people are certain that they are going to see a scalar field which, at the very least, looks very much like the single Higgs boson in minimal models.

In my opinion, there is a problem somewhere else : even if they do not see any signal, they are already plethora theoreticians which will be happy. There are models without Higgs, there are models for which the Higgs is much heavier etc...

 

[yquantumjumps]

Why does the concept renormalisable make things acceptable? It is no more than sweeping things under the carpet by saying infinity - infinity=0.
And at least half a dozen prominent physicists have so described it in discussion -- though no doubt in writing they would have been more circumspect. if you know of a real justification i would be glad to hear iit.
ernie

Happy New Year,

I understand the concern above with renormalizability , when working on our degrees we are encouraged to take paths that have been proven, this is not said but assumed & we all know that when working on the paper it must be outside the perimeters of the ordinary for us to receive the degree in which we work so hard for. I agree on sure footing and tested, & productive results which brings application to a research project.

But, on the other side of this coin is a paradox of discovery that needs to be researched, example Higgs we must think outside the box and search not leaving one mathematical tool that could aide us in finding what is so desperately needed to verified some problematic issues in the Standard Model.

Mathematics is not the final word, but it is a universal language in which we can communicate across this small globe we call home. We cannot always take the comfortable position in our search. Yes Non- Commutative Geometry is a new approach, but has promise. [NCG]

My one concern is we begin to find fault with the process, instead of seeking and encouraging by helping those in the tasks at hand.


BGE

 

[Ernies]

Happy New Year,
I understand the concern above with renormalizability , when working on our degrees we are encouraged to take paths that have been proven, this is not said but assumed & we all know that when working on the paper it must be outside the perimeters of the ordinary for us to receive the degree in which we work so hard for. [end of qouote]
My Prof must have been most unusual. When I gradusted in 1950, his parting lecture was on the lines of "Don't believe the books: don't even believe me----- not till you understand what is said and its justification!"
My point is simply that renormalisation is no more than a working hypothesis, no more at all. Yet as you can see from earlier replies it is regarded as a fundamental and well-established law.

I agree on sure footing and tested, & productive results which brings application to a research project.
But, on the other side of this coin is a paradox of discovery that needs to be researched, example Higgs we must think outside the box and search not leaving one mathematical tool that could aide us in finding what is so desperately needed to verified some problematic issues in the Standard Model.
Mathematics is not the final word, but it is a universal language in which we can communicate across this small globe we call home. We cannot always take the comfortable position in our searcand h. Yes Non- Commutative Geometry is a new approach, but has promise. [NCG]
My one concern is we begin to find fault with the process, instead of seeking and encouraging by helping those in the tasks at hand.

BGE

The trouble is that the the operation of renormalisation is itself mathematical, and requires justification. Otherwise I agree with you. Without a jump in thedark nothing new is found. But after 50-odd years... Ernie

 

[Kea]

Apparently Alain Connes has made quite profound progress in understanding the nature of the process of renormalization.

Yes (along with Marcolli and Kreimer), but this hardly gives us confidence in the SM Higgs mechanism. Au contraire! The delicateness of these new methods, which cannot be applied to the full SM, leads one simply to wring one's hands in eager anticipation of their non-Abelian extensions.

 

[Careful]

**It is certainly more than just that for sure ! Renormalizability is a very important issue, and everybody agrees that it is not fully understood. But unless you pretend to have theory valid at every energy scale AND finite, you need renormalization. **

Why ?? Why do you need to have a theory which is valid on ALL energy scales (UV cutoff to infinity) ? It seems to me that such theory would be only possible when nature presents us with a cutoff where the continuum breaks down (i.e. unbreakable units enter the stage). Why is it unnatural that low energy physics depends upon what happens at high energies (I understand of course why this would be desirable but I do not see why this should be a logical necessity) ?

Renormalization means for example : lack of knowledge of spacetime structure of matter. It will still leave us with the wrong theory at sufficiently high energy scales (and I wonder when we get to generation Z of the standard model ) so why bother about these ? unfortunately, renormalization also seems to tell us (if I remember correctly) that the demand that physical quantities do *not* depend upon the high energy scale is NECESSARY in order to get the correct results out of the relevant QFT (which makes me doubt about the theory at hand in the first place).

To repeat myself, it seems to me that renormalization should not be an issue in a satisfactory theory of fundamental interactions...

 

[Ernies]

**It is certainly more than just that for sure ! Renormalizability is a very important issue, and everybody agrees that it is not fully understood. But unless you pretend to have theory valid at every energy scale AND finite, you need renormalization. **
(SNIP)
To repeat myself, it seems to me that renormalization should not be an issue in a satisfactory theory of fundamental interactions...

The fact that it is a 'workaround', and no more, surely means that it IS an issue. Quite apart from Godel's Theorem, it precludes a sensible 'theory of everything'. (That is until a satisfactory justification is given) Otherwise it is like a witch's spell that happens to work. Useful.

ernie

 

[Careful]

The fact that it is a 'workaround', and no more, surely means that it IS an issue. Quite apart from Godel's Theorem, it precludes a sensible 'theory of everything'. (That is until a satisfactory justification is given) Otherwise it is like a witch's spell that happens to work. Useful.
ernie

What I meant is that it should not appear in a theory of everything (and be replaced by something better), so I guess we agree. The Godel argument is correct, however for me a theory of ``everything´´ is one which provides a consistent set of rules which covers all unbaised experimental data known so far and clearly satifies Occam's razor. Of course, Godel's theorem does not pose necessarily a problem here.

Cheers,

Careful

 

[Haelfix]

Renormalization is not just theoretical, it is experimental fact, mathematical certainty and pretty much self evident at least in a few situations.

There are models in condensed matter which we can solve exactly (usually in 2+1 dimensions or on lattices) and its quite apparent what renormalization means in those contexts, and why its needed in those particular series approximation.

If you want my personal opinion, there is nothing mysterious or bizarre about renormalization in general, when Wilson figured out the renormalization group in the mid seventies I think it became pretty apparent what it entailed.

You can point to mathematical problems with field theory before renormalization (and indeed straight to some of the core ideas which are mathematically tenous) but as is often the case, the end result is usually far better defined than what we started with.

 

[Careful]

**Renormalization is not just theoretical, it is experimental fact, mathematical certainty and pretty much self evident at least in a few situations. **


?? What is it that makes renormalisation an experimental fact ? :
It is a mathematically well defined procedure, but that it equivalent to saying that a donkey should have two ears and one tale

**
There are models in condensed matter which we can solve exactly (usually in 2+1 dimensions or on lattices) and its quite apparent what renormalization means in those contexts, and why its needed in those particular series approximation. **

Sure, I did not contest that it is mathematically appearent what happens *perturbatively* at the level of the Feynman series. However, you seem to have entirely missed the *physical* points I have raised. Also, you should explain to me WHY renormalisation is necessary a priori (and do not come up with the universality arguments) since it seems entirely plausible to me that low energy physics depends upon what happens at high energies. Moreover, you also seem to have missed the point that unless you write out a theory for UNBREAKABLE units, your renormalized theory shall always give the wrong answer at sufficiently high energies. By the way, in 2+1 dimensions, do you manage to renormalize ALL correlation functions ? I am sure that finding a Hilbert space representation (which is actually what is needed) is far too ambitious.

** If you want my personal opinion, there is nothing mysterious or bizarre about renormalization in general, when Wilson figured out the renormalization group in the mid seventies I think it became pretty apparent what it entailed. **

Yes, and it was at the same time clear that this procedure cannot be used for a theory which has the ambition to provide a deeper insight into the nature of matter. Ernies is right in pointing out that it is a useful tool to cure sick theories.

** You can point to mathematical problems with field theory before renormalization (and indeed straight to some of the core ideas which are mathematically tenous) but as is often the case, the end result is usually far better defined than what we started with.[/QUOTE] **

Your beautiful renormalization procedure did unfortunately not help yet to produce a single well defined interacting QFT in 3+1 dimensions

One should not be afraid to abandon a tool in those circumstances (unified theory) where it is clear that something better is needed.

Cheers,

Careful

 

[marlon]

?? What is it that makes renormalisation an experimental fact ? :

Well, just look at the work of http://nobelprize.org/physics/laureates/1999/index.html. They used renormalization theory to "cure" the divergences in the electroweak theory. I especially recommend their Nobel Lectures.

Also, you should explain to me WHY renormalisation is necessary a priori (and do not come up with the universality arguments)

Is this a raethorical question ?

since it seems entirely plausible to me that low energy physics depends upon what happens at high energies.

What exactly do you mean by that ? The evolution of the coupling constant in terms of energyscale is described by renormalization, but that's the only connection between low and high energy (as far as i can see). How can you link perturbative and non-perturbative behaviour ?

your renormalized theory shall always give the wrong answer at sufficiently high energies.

What field theory are you talking about ?

One should not be afraid to abandon a tool in those circumstances (unified theory) where it is clear that something better is needed.
Cheers,
Careful

Do you have a suggestion ?

regards
marlon

 

[Careful]

**Well, just look at the work of http://nobelprize.org/physics/laureates/1999/index.html. They used renormalization theory to "cure" the divergences in the electroweak theory. I especially recommend their Nobel Lectures. **

Sigh, what a boring argumentation (don't you think I know 't Hoofts and Veltman's lecture ? ). If you just don't have any intelligent answer, then don't use such argumentation (perhaps you could imagine that even some of these people might agree with my thesis here).

** Is this a raethorical question ? **

No, it isn't ! I just excluded one particular answer (which I do not find very convincing) to this question simply to make the conversation more efficient.

**
What exactly do you mean by that ? The evolution of the coupling constant in terms of energyscale is described by renormalization, but that's the only connection between low and high energy (as far as i can see). **

The renormalization equation on the coupling constants expresses that the resulting theory should be finite (in the sense that N - point functions should be finite) and not depend upon the high energy (UV) cutoff of the QFT at hand. Why should this be a requirement ??

** How can you link perturbative and non-perturbative behaviour ? **

That was not the issue and is a far more difficult question to answer.

** What field theory are you talking about ? **

For example: the original version of the standard model (I thought one is playing around with SU(9) or SU(10) theories already now).

**Do you have a suggestion ? **

Yes: study continuum classical models for elementary particles and their stability.

Cheers,

Careful

 

[marlon]

Sigh, what a boring argumentation (don't you think I know 't Hoofts and Veltman's lecture ? ). If you just don't have any intelligent answer, then don't use such argumentation

Don't turn things around just because you have no answer, please. You know very well why i posted this remark on the 1999 Physics Nobel Prize winners. I ilso should add the work of http://nobelprize.org/physics/laureates/2004/. Renormalization works. "Point final"

(perhaps you could imagine that even some of these people might agree with my thesis here).

Don't make useless speculations to impress people. It doesn't work.

The renormalization equation on the coupling constants expresses that the resulting theory should be finite (in the sense that N - point functions should be finite) and not depend upon the high energy (UV) cutoff of the QFT at hand. Why should this be a requirement ??

Err, because it works

That was not the issue and is a far more difficult question to answer.

No it is not, the answer has been given by these guys when it comes to electroweak interactions and QCD

For example: the original version of the standard model (I thought one is playing around with SU(9) or SU(10) theories already now).

No, no, i meant to ask what ESTABLISHED field theories ?
You are just speculating

Just keep in mind that mindless speculations are not allowed in this forum. If you make a point that does not correspond to mainstream physics, make sure that you can proof it at any time. Just to be clear, this does not imply that new ideas cannot be discussed here, they CAN. They just have to be discussed in an intelligent manner.

regards
marlon

 

[Careful]

** Don't turn things around just because you have no answer, please. You know very well why i posted this remark on the 1999 Physics Nobel Prize winners. I ilso should add the work of http://nobelprize.org/physics/laureates/2004/. Renormalization works. "Point final"
Don't make useless speculations to impress people. It doesn't work.
Err, because it works **

Sigh ... if there is one person who wants to impress people by quoting names of nobel prize winners, it is you. The rest of your comments are just too simplistic. Moreover, you seem to have missed my comments that it is NOT sufficient to be able to calculate the correlation functions: one should dispose of an Hilbert space representation.

**No it is not, the answer has been given by these guys when it comes to electroweak interactions and QCD **

As I said, this is nontrivial (as you should know ). In QCD something like asymptotic freedom is needed to do that job. As far as the weak interactions go, they are *not* nonperturbatively renormalizable AFAIK. In gravity for example, people are even trying to go further: they argue that a theory which is not even perturbatively renormalizable might actually be nonperturbatively renormalisable.


**No, no, i meant to ask what ESTABLISHED field theories ? **

The standard model is pretty established no ? And I know for a fact that people in MEANSTREAM physics (which you love so much ) are researching unified models with higher gauge groups, so this is no speculation but very up to date information.


** Just keep in mind that mindless speculations are not allowed in this forum. If you make a point that does not correspond to mainstream physics, make sure that you can proof it at any time. Just to be clear, this does not imply that new ideas cannot be discussed here, they CAN. **

This is far from mindless speculation It is pretty obvious that the construction of realistic matter models (and the stability study thereof) are a key step to banning renormalization. For your reference: the late A.O. Barut (amongst many) has uttered the same idea a long time ago and actually has done quite some work on it (realistic electron models for example).

Cheers,

Careful

 

[marlon]

Sigh ... if there is one person who wants to impress people by quoting names of nobel prize winners, it is you. The rest of your comments are just too simplistic.

No, because they are a crystal clear proof of what i am trying to say.

Moreover, you seem to have missed my comments that it is NOT sufficient to be able to calculate the correlation functions: one should dispose of an Hilbert space representation.

Look, you cannot just make a vague statement to proof your point. Where are the formula's ? The references ? Please react clearly to what i am trying to say to you.

In QCD something like asymptotic freedom is needed to do that job.

But how do you think this principle was described and proved ? You might want to read some of the references i gave you, since clearly you are not familiar with their content.

In gravity for example, people are even trying to go further: they argue that a theory which is not even perturbatively renormalizable might actually be nonperturbatively renormalisable.

Let's be clear, there is NO established field theory for gravity so you cannot bring this up just to state that "renormalization is not ok". Restrain yourself to mainstream physics.

The standard model is pretty established no ?

Sure it is. Now you answer this, what good did renormalization do in the electroweak interaction and QCD, hu ?

And I know for a fact that people in MEANSTREAM physics (which you love so much ) are researching unified models with higher gauge groups, so this is no speculation but very up to date information.

Unless a theory has passed the required stages (refereeing, experimental backup) it does not belong to mainstream physics. Besides, explain what you mean by the notion "higher gauge groups".

This is far from mindless speculation It is pretty obvious that the construction of realistic matter models (and the stability study thereof) are a key step to banning renormalization.

Clearly, you are misinterpreting. renormalization does not need to be banned because it has proven it's value. We only need to look further at the problems related to renormalization. This is something entirely different.

For your reference: the late A.O. Barut (amongst many) has uttered the same idea a long time ago and actually has done quite some work on it (realistic electron models for example).

References please...References to peer reviewed articles...Otherwise don't make such statements.

marlon

 

[Careful]

**
But how do you think this principle was described and proved ? You might want to read some of the references i gave you, since clearly you are not familiar with their content. **

Of course through renormalization (I did not deny that) I merely said that the property of asymptotic freedom improves the theory (that is no Landau poles or divergences of the coupling constants at some high energies as happens in QED).
It is understood that asymptotic freedom in the strong interactions is what makes QCD nonperturbatively renormalizable, while QED is not.

**
Let's be clear, there is NO established field theory for gravity so you cannot bring this up just to state that "renormalization is not ok". Restrain yourself to mainstream physics. **

I did not use this as an argument against renormalization (learn to read) : I merely used this to diversify on your false claim that perturbative renormalizable implies nonperturbative renormalizable which you made three posts ago (and which is wrong as happens in the weak interactions AFAIK).

** Sure it is. Now you answer this, what good did renormalization do in the electroweak interaction and QCD, hu ?**

Ah, it made the theory sensible. But I am not denying that it is a useful tool, but a limited one which cannot be used for unification Again, you did not listen.


** Unless a theory has passed the required stages (refereeing, experimental backup) it does not belong to mainstream physics. Besides, explain what you mean by the notion "higher gauge groups". **

Higher dimensional principal fibre bundle connections ! Jee, you should know that.

** Clearly, you are misinterpreting. renormalization does not need to be banned because it has proven it's value. We only need to look further at the problems related to renormalization. This is something entirely different. **

Wrong, we do not have any rigorous interacting QFT so far in 3+1 dimensions as is WELL KNOWN (for a confirmation of this statement, see the paper of Nicolai, Peeters and Zamaklar on loop quantum gravity) and it also well accepted that computing correlation functions is NOT enough. And I did not say it has to be banned: I merely said that it cannot serve for a theory of ``everything´´. Again, you fail to read correctly.

**
References please...References to peer reviewed articles...Otherwise don't make such statements. **

If it makes you happy, I shall look them up (but promise to READ them at least.) but again, these things are at least seven years old.


Cheers,

Careful

 

[Hans de Vries]

your renormalized theory shall always give the wrong answer at sufficiently high energies.

Any theory (= physical model) goes wrong at sufficiently small distances
(high energies). To go smaller you need the next model, and the next one,
et-cetera.

Yes, and it was at the same time clear that this procedure cannot be used for a theory which has the ambition to provide a deeper insight into the nature of matter. Ernies is right in pointing out that it is a useful tool to cure sick theories.

Hmmm, The infinite field energies of Coulomb point charges doesn't make
Electro Magnetism a 'sick' theory.

One should not be afraid to abandon a tool in those circumstances (unified theory) where it is clear that something better is needed.
Cheers,
Careful

The requirement for a theory to be renormalizable has been proven as
being on of the best tools to filter out (experimentally) correct physical
models.Regards, Hans

 

[Careful]

Hi Hans,

**Any theory (= physical model) goes wrong at sufficiently small distances
(high energies). To go smaller you need the next model, and the next one,
et-cetera. **

Correct.

**
The requirement for a theory to be renormalizable has been proven as
being on of the best tools to filter out (experimentally) correct physical
models.
**

That is true (I never disputed that) . Consider now your first remark : if you know the validity of the theory to end at some energy scale below the Planck energy, why should you bother about physics (in the same model) above some related cutoff? In either, why would you be interested in taking the continuum limit (perturbatively in most cases) in which you hold fixed the physical predictions of the theory and send the lattice spacing to zero (and shift the bare coupling constants to infinity) ? I mean, the only thing one should perhaps worry about is, given a physically motivated cutoff and bare coupling constants, that the physical coupling constants of the effective theories dictated by the Wilson RNG flow match observation. Why worry whether your can remove in perturbation series order by order all infinities by eventually adding a finite number of extra terms in the bare Lagrangian ?

Let me try to convey what is so bizarre about this game: suppose I take two bundles of particles which I am going to scatter (think of the particles as realistic non pointlike objects). When the impact velocity gets higher, more degrees of freedom of the particles are going to be ``activated´´ (particles are all in all not hard pointlike nuggets). At small kinetic energies, one can consider them like hard nuggets and the diameter of the particle is a well motivated length cutoff (and only one degree of freedom of the particle is activated). Now, increasing the velocity, the particles might not break yet, but the scattering might get inelastic and internal degrees of freedom inside the particle have to be activated (sub units - for example quarks in protons), at even higher energies, the particle breaks and the subunits become relatively independent of each other (like the quarks) and so on ... . Now, it is of course NOT the case that these subunits (eg quarks) - which are traditionally linked to gauge symmetries - NEED to determine NEW FUNDAMENTAL interactions (field strengths of gauge connections). But this exactly what particle physics does when it incorporates higher gauge fibre bundles. In the same spirit, it is nonsensical to look at energy scales in Lagrangian models for protons when the quarks need to be activated ! So, why study the continuum limit of a theory when you know that it is a priori wrong (and sick because basically what you say is that firing with arbitrary energy at a particle is leaving it intact) ?! So, in this logic one can never arrive at a fundamental theory : and neither can one make predictions about the next generation of particles we can expect to emerge at certain energies. Moreover, we are only increasing the number of ``fundamental´´ forces (more and more degrees of freedom in the gauge connection). That is one reason why I suggest that studying the full stability of continuum particle models can truly learn us something about nature and sweep the issue of renormalisability under the carpet. Such procedure does not add degrees of freedom in the interactions, but puts them in the complexity of the matter/charge distribution of the particle model which obeys - to start with - only the laws of GR and EM.

Hope that I made it clear.

Cheers,

Careful

 

[Careful]

By the way, anyone who is interested in a good introduction to renormalization, check out http://math.ucr.edu/home/baez/renormalization.html

Cheers,

Careful

 

[Ernies]

Well, just look at the work of http://nobelprize.org/physics/laureates/1999/index.html. They used renormalization theory to "cure" the divergences in the electroweak theory. I especially recommend their Nobel Lectures.
Is this a raethorical question ?

1.That an ad hoc "cure" was needed surely points to weakness both of the problem and the "cure".Sure, it was an achievement, but as I said 'ad hoc'.

2. Careful's statement was not a question: nor was it rhetorical.
Normalisation is not 'a priori' obvious.

3. I originally asked "Why does it work?". No-one has answered.

ernie

 

[Careful]

Hi Ernie,

Your question : ``why does renormalization work ?´´can be seen from many points of view. The one I developped in the previous post (and I think was also Wilson's) basically boils down to the statement that taking the continuum limit should not be done in the first place. Given a certain cutoff and bare coupling constants which we fit to get the correct predictions, it seems plausible to think that any nonrenormalizable theory could be replaced by a renormalizable one on the effective scales we observe it given the fact that the effective coupling constants in front of the nonrenormalizable terms go to zero anyway in the IR limit.

Now, you might not like this fine tuning, but in the same way I do not like that the bare couplings go to infinity either. On the other hand, if you insist on taking the continuum limit, then it seems to me that you eliminate divergences due to the scattering of *pointlike* particles which is *elastic* at arbitrary high frequency modes. Now, for non renormalizable theories an infinite number of new interactions is necessary to achieve this (due to nonlinearities in the interactions which are non polynomial).


Cheers,

Careful

 

[Haelfix]

Im a little confused about what the argument is exactly.

If you are saying that the RNG flow equations are fundamental, you won't get an argument out of me. The nature of these equations determines exactly when, where and what renormalization means (indeed what it means at a nonperturbative level).

Yes, sometimes these equations say: 'hi, I am flowing to a nontrivial nongaussian fixed point' in which case all that means is you can't renormalize the theory perturbatively, but the theory isn't necessarily doomed as it could still make sense nonperturbatively.

All I am saying is there are exactly solvable field theories that have been experimentally verified, whereby the renormalization procedure is perfectly well understood at a physical level. We know exactly what it means and we can *see* why we have to use it to match the nonperturbative *result*.

 

[Careful]

** I am a little confused about what the argument is exactly.
If you are saying that the RNG flow equations are fundamental, you won't get an argument out of me. **

They are *not* fundamental, they are merely a devise to probe (at some energy scale) the effective (physical) coupling constants of a theory given a finite lattice cutoff and some bare coupling constants. Under fundamental, I understand the objective ``bare´´ theory itself and not how we percieve it when we probe space at some characteristic length scale.


**The nature of these equations determines exactly when, where and what renormalization means (indeed what it means at a nonperturbative level). **

True, but not all information is given to you by UV fixpoints of the RNG flow AFAIK. In QED, the electron charge diverges at high energies (Landau pole), and becomes null in the IR limit : QED is perturbatively renormalizable but not nonperturbatively.

**
Yes, sometimes these equations say: 'hi, I am flowing to a nontrivial nongaussian fixed point' in which case all that means is you can't renormalize the theory perturbatively, but the theory isn't necessarily doomed as it could still make sense nonperturbatively. **

True, and that amounts for example in the QFT approach to QG (and such nontrivial fixpoints are found already).

**
All I am saying is there are exactly solvable field theories that have been experimentally verified, whereby the renormalization procedure is perfectly well understood at a physical level. We know exactly what it means and we can *see* why we have to use it to match the nonperturbative *result*. **

True, the standard model is non-perturbatively renormalizable (thanks to the Higgs AFAIK - and the Landau pole of QED is dissolved). All I wanted to point out is that taking the continuum limit is (a) *not* a priori necessary (but the RNG flow still remains a useful toy obviously) (b) the ideas behind *renormalization* (and not necessarily RNG) and gauge symmetries are *not* adequate for unification in my opinion (as I explained) since it is in a clear sense an *a posteriori* fitting, it can never make *predictions* about *new building blocks* at higher energies *a priori* (by construction).

Furthermore, it does not provide me with any *physical* insight of the *details* of the scattering process (I agree that some understanding can be gained from regularizing feynman diagrams but that is by far not sufficient in my view). I did not get any comments to these thoughts (in which I am far from being alone btw). I agree with you that it works but NOT that it is a *necessary* cure, IMO the problem is to be found in the theory you start with in the first place or in the *procedure* of second quantization itself.

Cheers,

Careful

 

[Careful]

Hi Haelfix,

Let me ask you a question (I will put aside the lack of Hilbert space representations in interacting QFT's) - others are also free to answer of course - : what possible conclusions would *you* reach if the Higgs were not to be found at *reasonable* energy scales (there is a limit to the argument : ``we have to look at higher energies´´ you know) ? For example: would it tell you something about (a) the a priori necessity of renormalization (b) the bare lagrangian you start with (c) second quantization (d) something even far more radical ?

Cheers,

Careful

 

[Ernies]

Hi Ernie,
Your question : ``why does renormalization work ?´´can be seen from many points of view. The one I developped in the previous post (and I think was also Wilson's) basically boils down to the statement that taking the continuum limit should not be done in the first place. Given a certain cutoff and bare coupling constants which we fit to get the correct predictions, it seems plausible to think that any nonrenormalizable theory could be replaced by a renormalizable one on the effective scales we observe it given the fact that the effective coupling constants in front of the nonrenormalizable terms go to zero anyway in the IR limit.
Now, you might not like this fine tuning, but in the same way I do not like that the bare couplings go to infinity either. On the other hand, if you insist on taking the continuum limit, then it seems to me that you eliminate divergences due to the scattering of *pointlike* particles which is *elastic* at arbitrary high frequency modes. Now, for non renormalizable theories an infinite number of new interactions is necessary to achieve this (due to nonlinearities in the interactions which are non polynomial).
Cheers,
Careful

Thank you for taking so much trouble. I do take your points, though, like you, I am not entirely happy with them.
To be frank, some of the correspondents' attitudes remind me of that famous book where each contributor started with "There is only one correct interpretation of Quantum Theory..." but each gave a completely different version. (I cannot recall the title, but it was based on BBC radio broadcasts many years ago). You, I must congratulate on admitting and analysing the uncertainties. Thank you again. Since we are now unlikely to get any further, I shall bow out of the dispute.
cheers!
Ernie

 

[Haelfix]

I think we're talking past each other here.

WHen I say RNG is fundamental, I mean given some field theory (any field theory), it tells us something very concrete about the nature of the *real* result, eg the nonperturbative *thing* which is what we want afterall not just the series approximation.

Now as to which field theory ultimately is fundamental with regards to what nature is about, well I am not sure if we will ever find such a thing that is both the right answer as well as being manifestly correct at all energy scales. It could be entirely possible for instance, that QED is the last word on the subject. THe landau pole can be pushed up to very high energies, and we could maybe just say 'well the universe never goes to infinite energy, ergo qed is just what it is, despite a purely mathematical singularity'.

Ok, I don't happen to believe that, just like I don't believe QCD is the final word either (it is asymptotically free, and more or less perfectly valid naively at all energy scales) but its easy to just add more degrees of freedom (in fact you can always add more terms to any theory you can think off, losing gauge symmetry and renormalization makes this worse, not better).

So Why is 'gauge theory and renormalization fundamental?', I don't know but in the formers case it appears in every important physical case we know off. In the latters, well pretty much (with a few exceptions that I mentioned), these are the only instances of reasonably complex field theories where we can actually predict things (and they are also empirically hundreds of times more likely to appear in nature, for whatever reason than their nonrenormalizable counterparts).