A Geometric Approach to the Standard Model, Greg Trayling

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SUMMARY

The discussion centers on Greg Trayling's geometric approach to the Standard Model of particle physics, specifically utilizing the Clifford algebra \mathcal{CL}_7. This model reveals that gauge symmetries and charge assignments of fundamental fermions emerge from extra space-like dimensions. The coupling constants are shown to satisfy the relationship g_s/g = g'/g = \sqrt{3/5}, aligning with SU(5) grand unification principles without the need for master groups. Additionally, the Higgs isodoublet field is derived naturally within this framework, supported by a matrix representation of \mathcal{CL}_7 for computational purposes.

PREREQUISITES
  • Understanding of Clifford algebras, specifically \mathcal{CL}_7
  • Familiarity with gauge symmetries in particle physics
  • Knowledge of the Standard Model and its components
  • Basic concepts of grand unification theories, particularly SU(5)
NEXT STEPS
  • Explore the implications of extra dimensions in theoretical physics
  • Study the derivation and significance of the Higgs isodoublet field
  • Investigate the role of preons in particle physics models
  • Review related articles that cite Trayling and Baylis's work for further insights
USEFUL FOR

This discussion is beneficial for theoretical physicists, researchers in particle physics, and anyone interested in advanced models of the Standard Model, particularly those exploring geometric frameworks and grand unification theories.

CarlB
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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
 

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