arXiv 0901.42302009-01-27hep-th

局部规范SO（3，3）对称群中六维时空中的Dirac方程和非手征电弱理论

The Dirac equation and a non-chiral electroweak theory in six dimensional spacetime from a locally gauged SO(3,3) symmetry group

C. A. Dartora, G. G. Cabrera

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摘要：

在具有3个类时坐标和3个类空坐标的6维时空中，提出了一个关于电弱相互作用（无手征）的玩具模型。时空间隔$ds^2=dx_μdx^μ$在对称群SO（3，3）下是左不变的。我们得到狄拉克伽玛矩阵的六维形式$Γ_μ$，并写出一个类似狄拉克的拉格朗日密度${\cal L}=i \barψ Γ^μ\nabla_μψ$。旋量$ψ$被分解为两个狄拉克旋量，$ψ_1$和$ψ_2$，我们解释为电子和中微子场，分别。在六维时空中，电子场和中微子场以一种自然的方式合并。SO（3，3）Lorentz对称群必须局部破缺为可观测SO（1，3）Lorentz群，且只有一个可观测的时间分量$t_z$。$t_z$轴在时空的所有点上可能都不相同，而SO（3，3）时空对称群局部破缺为SO（1，3）洛伦兹群的效应被观测者认为是规范场的存在。质量的起源可以归因于剩下的两个隐藏的类时维。我们将质量和规范相互作用的起源解释为额外时间维度的结果，而不需要所谓的希格斯机制来产生质量。此外，我们能够给出一个几何意义的电磁和非阿贝尔规范对称性。

英文摘要：

A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_μdx^μ$ 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, ${\cal L}=i \barψ Γ^μ\nabla_μψ$. The spinor $ψ$ is decomposed into two Dirac spinors, $ψ_1$ and $ψ_2$, which we interpret as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields are then merged in a natural manner. The SO(3,3) Lorentz symmetry group must be 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. The origin of mass may be attributed to the remaining two hidden timelike dimensions. We interpret the origin of mass and gauge interactions as a consequence of extra time dimensions, without the need of the so-called Higgs mechanism for the generation of mass. Further, we are able to give a geometric meaning to the electromagnetic and non-abelian gauge symmetries.

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