On the problem of choosing subgroups of Clifford algebras for applications in fundamental physics. (English) Zbl 1472.15034
Summary: Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. An algebraist’s perspective on the many subgroups and subalgebras of Clifford algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations of fermions and the symmetry-breaking of the weak interaction seem to emerge naturally from an extension of the Dirac algebra from complex numbers to quaternions.
MSC:
| 15A67 | Applications of Clifford algebras to physics, etc. |
| 15A66 | Clifford algebras, spinors |
| 81T11 | Higher spin theories |
| 81R40 | Symmetry breaking in quantum theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
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