The Dirac Equation in Six-dimensional SO(3,3) Symmetry Group and a Non-chiral 'Electroweak' Theory

Autor: G. G. Cabrera, C. A. Dartora
Rok vydání: 2009
Předmět:
Zdroj: International Journal of Theoretical Physics. 49:51-61
ISSN: 1572-9575
0020-7748
DOI: 10.1007/s10773-009-0177-9
Popis: We propose a model of electroweak interactions without chirality in a six-dimensional spacetime with 3 time-like and 3 space-like coordinates, which allows a geometrical meaning for gauge symmetries. The spacetime interval ds 2=dx μ dx μ is left invariant under the symmetry group SO(3,3). We obtain the six-dimensional version of the Dirac gamma matrices, Γ μ , and write down a Dirac-like Lagrangian density, $\mathcal{L}=i\bar{\psi}\Gamma ^{\mu }\nabla _{\mu }\psi$ . The spinor ψ can be decomposed into two Dirac spinors, ψ 1 and ψ 2, interpreted as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields appear as parts of the same entity in a natural manner. The SO(3,3) Lorentz symmetry group is locally broken to the observable SO(1,3) Lorentz group, with only one observable time component, t z . The t z -axis may not be the same at all points of the spacetime, and the effect of breaking the SO(3,3) spacetime symmetry group locally to an SO(1,3) Lorentz group, is perceived by the observers as the existence of the gauge fields. We interpret the origin of mass and gauge interactions as a consequence of extra time dimensions, without the need of introducing the so-called Higgs mechanism for the generation of mass. Further, in our ‘toy’ model, we are able to give a geometric meaning to the electromagnetic and non-Abelian gauge symmetries.
Databáze: OpenAIRE
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