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Higgs Field

  1. Dec 15, 2005 #1
    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
     
  2. jcsd
  3. Dec 15, 2005 #2

    Hans de Vries

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    Science Advisor

    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
     
    Last edited: Dec 15, 2005
  4. Dec 15, 2005 #3
    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
     
  5. Dec 18, 2005 #4
    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
     
  6. Dec 21, 2005 #5
    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
     
  7. Dec 21, 2005 #6
    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.
    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...
     
  8. Dec 29, 2005 #7
    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.

    Best,
    BGE
     
  9. Dec 29, 2005 #8
     
  10. Dec 29, 2005 #9

    Kea

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    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.

    :smile:
     
    Last edited: Dec 29, 2005
  11. Dec 30, 2005 #10
    **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 :biggrin: ) so why bother about these ? Unfortunatly, 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...
     
  12. Dec 30, 2005 #11
    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
     
  13. Dec 30, 2005 #12
    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
     
    Last edited: Dec 30, 2005
  14. Dec 31, 2005 #13

    Haelfix

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    Science Advisor

    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.
     
  15. Dec 31, 2005 #14
    **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 ? ::bugeye:
    It is a mathematically well defined procedure, but that it equivalent to saying that a donkey should have two ears and one tale :biggrin:

    **
    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 unfortunatly not help yet to produce a single well defined interacting QFT in 3+1 dimensions :biggrin:

    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
     
    Last edited: Dec 31, 2005
  16. Dec 31, 2005 #15
    Well, just look at the work of these guys. They used renormalization theory to "cure" the divergences in the electroweak theory. I especially recommend their Nobel Lectures.


    Is this a raethorical question ?

    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 ?

    What field theory are you talking about ?

    Do you have a suggestion ?:wink:

    regards
    marlon
     
  17. Dec 31, 2005 #16
    **Well, just look at the work of these guys. 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 ? :biggrin: ). 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 ?:wink: **

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

    Cheers,

    Careful
     
    Last edited: Dec 31, 2005
  18. Dec 31, 2005 #17
    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 these dudes. Renormalization works. "Point final"

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

    Err, because it works:rolleyes:

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

    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
     
  19. Dec 31, 2005 #18
    ** 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 these dudes. Renormalization works. "Point final"
    Don't make useless speculations to impress people. It doesn't work.
    Err, because it works:rolleyes: **

    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 :grumpy: ). 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 ? :rofl: And I know for a fact that people in MEANSTREAM physics (which you love so much :biggrin: ) 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 :rofl: :rofl: 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
     
    Last edited: Dec 31, 2005
  20. Dec 31, 2005 #19
    No, because they are a crystal clear proof of what i am trying to say.

    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.

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

    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.

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

    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".

    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.

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

    marlon
     
  21. Dec 31, 2005 #20
    **
    But how do you think this principle was described and proved ? You might wanna 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) :grumpy: 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 :grumpy: 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. :grumpy:

    ** 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
     
    Last edited: Dec 31, 2005
  22. Dec 31, 2005 #21

    Hans de Vries

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    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.

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


    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
     
  23. Jan 1, 2006 #22
    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) :smile:. 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 bizzare 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 truely 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
     
  24. Jan 1, 2006 #23
  25. Jan 1, 2006 #24
     
  26. Jan 1, 2006 #25
    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
     
    Last edited: Jan 1, 2006
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