Left-Ideals, Dirac Fermions and SU(2)-Flavour
| dc.creator | Witte, F. M. C. | |
| dc.date | 2006-12-27 | |
| dc.date | 2007-07-17 | |
| dc.date.accessioned | 2026-07-07T08:18:37Z | |
| dc.date.available | 2026-07-07T08:18:37Z | |
| dc.description | In this paper I reconsider the use of the left ideals of the even-grade subalgebra of spacetime algebra to describe fermionic excitations. When interpreted as rotors the general elements of an even-grade left-ideal describe massless particles in chiral flavour doublets. To study the application of these ideas to the standard Dirac formalism I construct a $2 \times 2$-matrix representation with bivector insertions for the Dirac algebra. This algebra has four ideals, and this approach clarifies how the identification of Dirac $\g_μ$-matrices with orthonormal basisvectors ${\bf e}_ν$ annihilates half of the ideals. For one possible choice of this mapping the remaining ideals the chiral left- and righthanded components of the fermion coincide with the even- and odd elements of spacetime algebra. | |
| dc.description | 15 pages, no figures, pdf-file | |
| dc.identifier | https://arxiv.org/abs/math-ph/0612081 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0612081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134493 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 94B27 (Primary); 17B81, 15A66 (Secondary) | |
| dc.title | Left-Ideals, Dirac Fermions and SU(2)-Flavour | |
| dc.type | text |