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Thread: Why are there 8 gluons?

  1. #1 Why are there 8 gluons? 
    Member iopst's Avatar
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    I've only read some popular science books on particle physics so my understanding is pretty basic.



    There are three colors and three anticolors. 3 x 3 will give us 9 gluons.

    Subtracting the red-antired and the other two leaves us with 6 gluons.



    Those science books only explain the first part but they don't explain how we wind up with 8.
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by iopst View Post
    I've only read some popular science books on particle physics so my understanding is pretty basic.



    There are three colors and three anticolors. 3 x 3 will give us 9 gluons.

    Subtracting the red-antired and the other two leaves us with 6 gluons.



    Those science books only explain the first part but they don't explain how we wind up with 8.
    The underlying reason is one of symmetry; quarks and gluons are described by QCD ( quantum chromodynamics ), which is a model built on a SU(3) gauge symmetry. For such a symmetry the number of force carriers equals the dimension of the so-called adjoint representation, which is for simple groups like SU(3) equal to N^2-1, i.e. 9-1=8.
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    Quote Originally Posted by Markus Hanke View Post
    The underlying reason is one of symmetry; quarks and gluons are described by QCD ( quantum chromodynamics ), which is a model built on a SU(3) gauge symmetry. For such a symmetry the number of force carriers equals the dimension of the so-called adjoint representation, which is for simple groups like SU(3) equal to N^2-1, i.e. 9-1=8.
    What is adjoint representation?
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    Quote Originally Posted by iopst View Post
    What is adjoint representation?
    That will take a mathematician to properly explain
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    Quote Originally Posted by Markus Hanke View Post
    That will take a mathematician to properly explain
    damn, you're the only one replying to my threads. thanks mark.

    all this jargon is making my mind swirl
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    Quote Originally Posted by iopst View Post
    damn, you're the only one replying to my threads. thanks mark.

    all this jargon is making my mind swirl
    Just give it some time, and others will pitch in as well.
    Some questions, like your last one, just don't have simple and straightforward answers, and I am not a mathematician, so I won't pretend that I can give a good answer to it.
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    Quote Originally Posted by Markus Hanke View Post
    Just give it some time, and others will pitch in as well.
    Some questions, like your last one, just don't have simple and straightforward answers, and I am not a mathematician, so I won't pretend that I can give a good answer to it.
    Yeah, there are too many pretenders around.
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    Quote Originally Posted by iopst View Post
    damn, you're the only one replying to my threads.
    I assume that you and "ostkef‎" from The Science Forum are one and the same. Did you read the reply there to this same question? Depending on what you consider an explanation, the article linked to there is probably as good as it gets, with an appeal to Occam's Razor (which I'll paraphrase as "a particle that doesn't interact with anything might as well be treated as not existing, so farewell, ninth gluon").
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    Quote Originally Posted by tk421 View Post
    I assume that you and "ostkef‎" from The Science Forum are one and the same. Did you read the reply there to this same question? Depending on what you consider an explanation, the article linked to there is probably as good as it gets, with an appeal to Occam's Razor (which I'll paraphrase as "a particle that doesn't interact with anything might as well be treated as not existing, so farewell, ninth gluon").
    yup. I try to "cast my net wide", to get a diverse range of opinions and replies.


    the popular physics books did mention the ninth gluon as "white"


    I don't really understand Baez's maths unfortunately.
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  10. #10  
    Administrator Markus Hanke's Avatar
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    the popular physics books did mention the ninth gluon as "white"
    A "white" gluon could not interact in any way with the other gluons and quarks, which is why it does not actually exist - hence there are only eight of them.
    QCD is notoriously difficult, and there are limits to what you can do and show without some pretty high-level maths.
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  11. #11  
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    Quote Originally Posted by Markus Hanke View Post
    QCD is notoriously difficult, and there are limits to what you can do and show without some pretty high-level maths.
    There's some similarity between photons and gluons, electric and color charge.

    It's interesting that we've had electroweak for 30 odd years, but no QECD yet.
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  12. #12  
    Administrator Markus Hanke's Avatar
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    but no QECD yet
    What is QECD ??
    I presume you are referring to a unification of QCD with the electroweak force - such a model would be called a GUT, a Grand Unified Theory. There are several candidate models for such a theory ( see Grand Unified Theory - Wikipedia, the free encyclopedia ), none of which is universally accepted. This is an area of ongoing research.
    The reason why we don't have an accepted GUT yet is simply one of complexity; the maths of such models is extremely difficult.
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    Quote Originally Posted by Markus Hanke View Post
    The underlying reason is one of symmetry; quarks and gluons are described by QCD ( quantum chromodynamics ), which is a model built on a SU(3) gauge symmetry. For such a symmetry the number of force carriers equals the dimension of the so-called adjoint representation, which is for simple groups like SU(3) equal to N^2-1, i.e. 9-1=8.
    A naive way of thinking of this might be to consider that there is a gluon as an intermediary between each pair of colors. This gives 23 pairs = 8 gluons.
    You can do everything right, strictly according to procedure, on the ocean and it'll still kill you, but if you're a good navigator at least you'll know where you were when you died.
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    Quote Originally Posted by Strange View Post
    A naive way of thinking of this might be to consider that there is a gluon as an intermediary between each pair of colors. This gives 23 pairs = 8 gluons.
    Sorry, I don't understand that analogy. My bad.



    Quote Originally Posted by Markus Hanke View Post
    What is QECD ??
    I presume you are referring to a unification of QCD with the electroweak force - such a model would be called a GUT, a Grand Unified Theory. There are several candidate models for such a theory ( see Grand Unified Theory - Wikipedia, the free encyclopedia ), none of which is universally accepted. This is an area of ongoing research.
    The reason why we don't have an accepted GUT yet is simply one of complexity; the maths of such models is extremely difficult.
    Not a GUT, because it doesn't include gravity. But a "simple" unification of QED with QCD. What's the best candidate for that currently?
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  15. #15  
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    Quote Originally Posted by iopst View Post
    Sorry, I don't understand that analogy. My bad.
    No, on second thoughts, I'm not sure it works
    You can do everything right, strictly according to procedure, on the ocean and it'll still kill you, but if you're a good navigator at least you'll know where you were when you died.
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  16. #16  
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    Quote Originally Posted by iopst View Post
    What is adjoint representation?
    On a group, a group element can act on a general group element by an action called conjugation.

    If the group is a Lie group, then this action is smooth and can be extended to a linear map on the tangent space at the identity (which is the Lie algebra associated to the Lie group) by taking the differential. That correspondence between x and a linear map on the Lie algebra is the adjoint representation of the group -- a homomorphism between the group itself and the group of non-singular linear operators on the Lie algebra.
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  17. #17  
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    Not a GUT, because it doesn't include gravity. But a "simple" unification of QED with QCD. What's the best candidate for that currently?
    I think there is a bit of misunderstanding with regards to the various terms here. So this is how it goes :

    QED ( Quantum Electrodynamics ) - electromagnetic interactions only
    QCD ( Quantum Chromodynamics ) - strong interactions only

    Salam-Glashow-Weinberg Model - electroweak interaction, i.e. a unification of electromagnetism and the weak interaction
    GUT ( Grand Unified Theory ) - unification of strong, weak and electromagnetic interactions
    TOE ( Theory of Everything ) - unification of all fundamental forces, including gravity

    As for the GUT, there is quite a large number of candidate theories, and no consensus as to which ones are physically viable. Many of these models aren't very well understood either. It is, as I noted before, an area of ongoing and active research.
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  18. #18  
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    Thanks for clarifying.

    I don't think TOE is an appropriate term for unification of all the fundamental forces, it just sounds too idealist.
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