# Thread: Why are there 8 gluons?

1. 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.  2. Originally Posted by iopst 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.  3. Originally Posted by Markus Hanke 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.  4. Originally Posted by iopst That will take a mathematician to properly explain   5. Originally Posted by Markus Hanke That will take a mathematician to properly explain all this jargon is making my mind swirl   6. Originally Posted by iopst 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.  7. Originally Posted by Markus Hanke 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.  8. Originally Posted by iopst 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").  9. Originally Posted by tk421 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.  10. 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.  11. Originally Posted by Markus Hanke 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.  12. 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.  13. Originally Posted by Markus Hanke 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.  14. Originally Posted by Strange 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. Originally Posted by Markus Hanke 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?  15. Originally Posted by iopst Sorry, I don't understand that analogy. My bad.
No, on second thoughts, I'm not sure it works   16. Originally Posted by iopst 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.  17. 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.  18. Thanks for clarifying.

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