Subgroups of Clifford algebras
Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 reserved pith:UFS6BKBFrecord.jsonopen to challenge →
read the original abstract
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on these groups and 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Sharp Lower Bound on the Minimax Risk for Multinomial Uniformity Testing via a Conditional Central Limit Theorem
The multinomial minimax risk for uniformity testing against $l_p$ alternatives converges exactly to $2Phi(-u^*/2)$ in the intermediate regime, proven via a conditional central limit theorem.
-
Surface Crevasse Evolution Observed Using Matched Field Processing and Source Relocation at Hansbreen, Svalbard
A MFP-plus-relocation workflow localizes surface icequakes on Hansbreen, producing crevasse propagation rates and diffusion coefficients of 0.47-0.55 m²/s interpreted as sustained subcritical crack propagation.
-
Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry
A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.
-
A Superalgebra Within: representations of lightest standard model particles form a $\mathbb{Z}_2^5$-graded algebra
Representations of lightest Standard Model particles form a Z_2^5-graded superalgebra isomorphic to H_16(C) and generated by division algebras.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.