A Geometric Approach to the Standard Model, Greg Trayling

[CarlB]

A Geometric Approach to the Standard Model
Greg Trayling, Dept of Phys, U. Windsor, Windsor, Ontario
A geometric approach to the standard model of the Clifford algebra $$\mathcal{CL}_7$$ is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra space-like dimensions. The bare coupling constants are found to obey $$g_s/g = g'/g = \sqrt{3/5}$$ consistent with $$SU(5)$$ grand unification but without invoking the notion of master groups. In constructing the Lagrangian density terms, it is found that the Higgs isodoublet field emerges in a natural manner. A matrix representation of $$\mathcal{CL}_7$$ is included as a computational aid.
http://www.arxiv.org/abs/hep-th/9912231

Also see:

A geometric basis for the standard-model gauge group
Greg Trayling, W. E. Baylis
Accepted for publication: J. Phys. A: Math. Gen. 9 Mar 2001
http://www.arxiv.org/abs/hep-th/0103137

I just found these obscure articles. My own attempts at rewriting the standard model are similar, except that I'm using preons and consequently don't need only one "extra space-like" dimension instead of the 4 used here.

Articles that cite the published article by Trayling and Baylis:
http://www.arxiv.org/abs/hep-th/0501222
http://www.arxiv.org/abs/hep-th/0412255
http://www.arxiv.org/abs/hep-th/0311045
http://www.arxiv.org/abs/gr-qc/0212041
http://www.arxiv.org/abs/hep-th/0203122

Carl

 

[LightHero]

os Montemayor and Tony G. Rheinboldt, "A Geometric Approach to the Standard Model", J. Phys. A: Math. Gen., 34(19), 2001, pp. 3911-3923.http://iopscience.iop.org/0305-4470/34/19/306

 

[sir-pinski]

Brannen


The geometric approach to the standard model presented by Greg Trayling is a fascinating and innovative way of understanding the fundamental particles and their interactions. By using the Clifford algebra \mathcal{CL}_7, Trayling is able to link the gauge symmetries and charge assignments of the fundamental fermions to a simple geometric model involving extra space-like dimensions. This not only provides a new perspective on the standard model, but also offers a potential solution to the problem of unifying the fundamental forces.

One of the most intriguing aspects of this approach is the emergence of the Higgs isodoublet field in a natural manner. The Higgs mechanism is a crucial component of the standard model and has been the subject of much research and speculation. However, with the geometric approach, the Higgs isodoublet field arises as a consequence of the underlying geometry, providing a more elegant and intuitive explanation.

Furthermore, the fact that the bare coupling constants obey g_s/g = g'/g = \sqrt{3/5} is consistent with SU(5) grand unification, but without the need for master groups, is a significant achievement. This not only simplifies the model, but also suggests a deeper underlying structure that may help to unify the fundamental forces.

I am also intrigued by the potential connections between this approach and the use of preons in other attempts to rewrite the standard model. It will be interesting to see how these different perspectives can be reconciled and potentially lead to a more complete understanding of the fundamental particles and their interactions.

Overall, Trayling's geometric approach to the standard model is a valuable contribution to the field of theoretical physics. It offers a fresh perspective and potential solutions to long-standing problems, and I look forward to seeing how it develops in the future.