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- W1750946763 abstract "It is shown how the old Cartan's conjecture on the fundamental role of the geometry of simple (or pure) spinors, as bilinearly underlying euclidean geometry, may be extended also to quantum mechanics of fermions (in first quantization), however in compact momentum spaces, bilinearly constructed with spinors, with signatures unambiguously resulting from the construction, up to sixteen component Majorana-Weyl spinors associated with the real Clifford algebra $Cl(1,9)$, where, because of the known periodicity theorem, the construction naturally ends. $Cl(1,9)$ may be formulated in terms of the octonion division algebra, at the origin of SU(3) internal symmetry. In this approach the extra dimensions beyond 4 appear as interaction terms in the equations of motion of the fermion multiplet; more precisely the directions from 5$^{th}$ to 8$^{th}$ correspond to electric, weak and isospin interactions $(SU(2) otimes U(1))$, while those from 8$^{th}$ to 10$^{th}$ to strong ones SU(3). There seems to be no need of extra dimension in configuration-space. Only four dimensional space-time is needed - for the equations of motion and for the local fields - and also naturally generated by four-momenta as Poincare translations. This spinor approach could be compatible with string theories and even explain their origin, since also strings may be bilinearly obtained from simple (or pure) spinors through sums; that is integrals of null vectors." @default.
- W1750946763 created "2016-06-24" @default.
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- W1750946763 date "2001-02-09" @default.
- W1750946763 modified "2023-09-27" @default.
- W1750946763 title "On Fermions in Compact momentum Spaces Bilinearly Constructed with Pure Spinors" @default.
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