Origin and Nature of Gauge Principle

[friend]

Not without referring to my unpublish(able) works. PM me if you want details.

Yes, if I were to just blurt out my summary or conclusions, it would seem speculative, and I'd get an infraction for my efforts. But maybe if I were to work backwards and quote my sources, then it might seem to fit.

So I'd like to start by noticing the relationship between the symmetries of the standard model and the Cayley-Dickson construction of the hypercomplex numbers. The Caley-Dickson construction seems to be an iterative process, and I'd like to show where this same iterative process comes from in the path integral of QM. So give me a few days to look up some references before I get too far.

 

[friend]

So I'd like to start by noticing the relationship between the symmetries of the standard model and the Cayley-Dickson construction of the hypercomplex numbers. The Caley-Dickson construction seems to be an iterative process, and I'd like to show where this same iterative process comes from in the path integral of QM. So give me a few days to look up some references before I get too far.

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Some have shown that these symmetries are related to the hypercomplex division algebras of the complex numbers, the quaternions, and the octonions. See here and here, which seem pretty well referenced. They equate the algebra of the quaternions to the algebra of the Pauli spin matices, and equate the algebra of the octonions to the algebra of the Gell-Mann λ matrices of the SU(3) symmetry. And also Sir Michael Atiyah Ph.D has discussed the relevance of these normed division algebras in the Youtube video here, starting at minute 29:00. The question remains, however, why these division algebras?

The Cayley-Dickson construction of the hypercomplex numbers is an iterative process such that the quaternions can be constructed from the complex numbers, and in the same way the octonions can be constructed from the quaternions. John Baez has an explanation of this iterative process here.

The Feynman path integral of a real, classical field, introduces a complex number to produce a quantum field, and this gives us the U(1) symmetry. This suggests to me that we could iterate the process by using a quaternion in the path integral of a complex field to get the SU(2) symmetry, and use an octionion in the path integral of a quaternion field to get the SU(3) symmetry. This is not present practice. But it does seem to suggest itself. Further study is required in order to say anything definitive. If applicable, this would explain the origin of the symmetries of the Standard Model.

 

[Ilja]

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Yes. But there is more to be explained: This group acts on the fermions in a very special way, which is described by the charges of the fermions. The number of the fermions and all the charges of all these fermions have to be explained too.

arXiv:0908.0591 proposes a solution, is published in Foundations of Physics, vol. 39, nr. 1, p. 73 (2009), but I have not received much reaction, except for an invitation to publish arXiv:0912.3892 in Reimer, A. (ed.), Horizons in World Physics, Volume 278, Nova Science Publishers (2012).

 

[kye]

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Some have shown that these symmetries are related to the hypercomplex division algebras of the complex numbers, the quaternions, and the octonions. See here and here, which seem pretty well referenced. They equate the algebra of the quaternions to the algebra of the Pauli spin matices, and equate the algebra of the octonions to the algebra of the Gell-Mann λ matrices of the SU(3) symmetry. And also Sir Michael Atiyah Ph.D has discussed the relevance of these normed division algebras in the Youtube video here, starting at minute 29:00. The question remains, however, why these division algebras?

The Cayley-Dickson construction of the hypercomplex numbers is an iterative process such that the quaternions can be constructed from the complex numbers, and in the same way the octonions can be constructed from the quaternions. John Baez has an explanation of this iterative process here.

The Feynman path integral of a real, classical field, introduces a complex number to produce a quantum field, and this gives us the U(1) symmetry. This suggests to me that we could iterate the process by using a quaternion in the path integral of a complex field to get the SU(2) symmetry, and use an octionion in the path integral of a quaternion field to get the SU(3) symmetry. This is not present practice. But it does seem to suggest itself. Further study is required in order to say anything definitive. If applicable, this would explain the origin of the symmetries of the Standard Model.

Do you or anyone knows of any papers at arxiv or peer reviewed paper in which free quarks can occurred from a certain gauge symmetry (from different vacuum condition) that is different from the basic symmetry where they are bound (or can't be isolated)?

 

[Berlin]

There are many examples where people try to relate the specific groups of the standard model to another 'higher' principle. But in many cases you do not get something new in explaining physics. So, those solutions more or less translate the assumption into another assumption without solving or predicting anything. I few years ago Christoph Schiller related the groups of the standard model to the three Reidemeister moves. When I saw this first, i thought, holy s*** this must be it, but in the end it did not explain much and merely created a new set of questions of the same size. However, the history of physics proves that reformulating a problem can be very strong, and indeed the basis for progress, which was more difficult in the other formulation. Let's hope we find one!

Berlin