Left-Ideals, Dirac Fermions and SU(2)-Flavour

dc.creatorWitte, F. M. C.
dc.date2006-12-27
dc.date2007-07-17
dc.date.accessioned2026-07-07T08:18:37Z
dc.date.available2026-07-07T08:18:37Z
dc.descriptionIn 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.description15 pages, no figures, pdf-file
dc.identifierhttps://arxiv.org/abs/math-ph/0612081
dc.identifierhttp://arxiv.org/abs/math-ph/0612081
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134493
dc.subjectMathematical Physics
dc.subject94B27 (Primary); 17B81, 15A66 (Secondary)
dc.titleLeft-Ideals, Dirac Fermions and SU(2)-Flavour
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