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bapowell

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phyzguy

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I think (looking for confirmation from this group) that right-handed (aka "sterile") neutrinos can still be added to the SM without adding new symmetries. Several groups are suggesting sterile neutrinos as dark matter candidates.

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I think (looking for confirmation from this group) that right-handed (aka "sterile") neutrinos can still be added to the SM without adding new symmetries. Several groups are suggesting sterile neutrinos as dark matter candidates.

Are you talking about the difference between the types of particles determined by the symmetries and the coupling constants (such as the mass and charge) that determine the strength of the interactions? Does each type of particle (determined by the symmetries) have only one coupling constant? Or can there be two particles with the same symmetries but different coupling constants?

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For example, is the Higg boson a particle predicted by the U(1)SU(2)SU(3) symmetry?

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Also, note that when we say the gauge group is SU(3)xSU(2)xU(1), realize that we don't mean that that's the absolute end all-be all gauge symmetry of the universe. It's the gauge symmetry of the effective field theory living below 1 TeV. It remains at higher energies, though perhaps as a subgroup of some bigger symmetry group, like SU(5) or SO(10). The jury is still out on that question.

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Also, note that when we say the gauge group is SU(3)xSU(2)xU(1), realize that we don't mean that that's the absolute end all-be all gauge symmetry of the universe. It's the gauge symmetry of the effective field theory living below 1 TeV. It remains at higher energies, though perhaps as a subgroup of some bigger symmetry group, like SU(5) or SO(10). The jury is still out on that question.

Thank you. That helps a lot. I guess what I'm trying to get at is whether given U(1)SU(2)SU(3), and the quantum mechanical formulism, is that enough information to identify all the fields and particles in the Standard Model and nothing else, well.. except maybe the Higgs boson?

The reason I ask is because some people think that the underlying math that gives rise to the U(1)SU(2)SU(3) symmetry is the existence of the complex numbers, the quaternions, and the octonions. So I wonder if the complex, quaternions, and octonions were explained from a more fundamental basis, would the SM be derivable on that basis? Thanks.

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tom.stoer

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To understand E(8) one would start with its algebra e(8) and the space E(8) acts on. But that doesn't help b/c the adjoint rep. of e(8) which could serve as a starting point is identical with its fundamental rep., therefore in a sense we are trying to describe E(8) in terms of E(8) which isn't a big step forward ;-)

http://math.ucr.edu/home/baez/octonions/

Afaik as I know all attempts to derive the SM from octonions failed.

http://arxiv.org/abs/0711.0770

http://arxiv.org/abs/0905.2658

http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything

Some time ago Garrett was reading posts and private messages here the "beyond forum", so perhaps you are able to ask hom directly regarding the status of his research.

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The current list of particles is theoretically adequate; we cannot know whether it is actually complete or not - the universe is a strange and mysterious place. After all, problem recognition is higher in the ladder of wisdom and innnovative ingenuity than correspondence in resolution. However, I highly doubt scientists have derived even the general knowledge concerning the entire family of various particles since more than 90% of the universe is presently unaccounted for, empirically speaking.

On the other hand, the SM, although probably not unique/complete, is definitely our best shot at understanding the subatomic domain for now. There are no better alternatives now and, as it seems, for all eternity.

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Regardless, no, once you have the group structure, you've fixed the gauge bosons of your theory, but you have yet to tell me the matter content.

Are you saying that the fermions are not accounted for in the U(1)SU(2)SU(3) symmetry? Or are you saying that just the strenght of the interactions between them is not accounted for by this symmetry?

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tom.stoer

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1) the matter fields can be bosons or fermions (up to spin 3/2 in SUSY-gauge theories)

2) they can live in various reprsentations of the gauge group (the SM matter fields live in the fundamental representation, but others are possible; adjoint fermions are studied in various models)

3) they can come in several copies, the so-called generations of the standard model

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1) the matter fields can be bosons or fermions (up to spin 3/2 in SUSY-gauge theories)

2) they can live in various reprsentations of the gauge group (the SM matter fields live in the fundamental representation, but others are possible; adjoint fermions are studied in various models)

3) they can come in several copies, the so-called generations of the standard model

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tom.stoer

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It's possible for there to be additional elementary-fermion generations or Higgs multiplets, for instance.

Fermions with chirality in their gauge interactions, like the elementary fermions, have their gauge-interaction parameters constrained by anomaly cancellation, but I can't think of anything additional at the moment.

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tom.stoer

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OK, then what physical properties does the U(1)SU(2)SU(3) symmetry determine in the SM? It's not the mass, nor the charge, nor the spin, not the speed, nor the position, nor the strength of interactions. Then what?

I understand that with symmetries come conserved "charges". So I suppose that the U(1)SU(2)SU(3) symmetry specifies the existence if the electromagnetic charge and the color charge and the, what is it, the weak force charge. So it tells us what interacts with what. But am I right to say that the SM symmetry does not specify the strength of those charges?

I understand that with symmetries come conserved "charges". So I suppose that the U(1)SU(2)SU(3) symmetry specifies the existence if the electromagnetic charge and the color charge and the, what is it, the weak force charge. So it tells us what interacts with what. But am I right to say that the SM symmetry does not specify the strength of those charges?

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