论文标题
基础红外的量子重力效应：低能量细胞结构常数和基本颗粒质量比的理论推导
Quantum gravity effects in the infra-red: a theoretical derivation of the low energy fine structure constant and mass ratios of elementary particles
论文作者
论文摘要
最近，我们提出了一种在八元时间时空上的基质增值的拉格朗日动力学作为基质值的拉格朗日动力学。该理论提供了将标准模型的内部对称性和重大验证统一的前景。我们解释了为什么即使在比普朗克量表小得多的能量下，这种量子引力动力学原则上都是必不可少的。动力学还可以预测低能标准模型的自由参数的值：Lagrangian中产生的这些参数与八分代的代数有关，该代数定义了基本的非交换时空的自由度发展。这些免费参数与特殊的Jordan代数$ J_3（8）$有关，该$描述了三个费米昂世代。我们使用费米子的八世代表示来计算该代数的特征方程的特征值，并将所得的特征值与已知的夸克和卵子的质量比进行比较。我们表明，特征值的比率正确地重现了已知质量比的[平方根]。这些特征值与痕量动力学拉格朗日式结合使用，还产生了低能量细胞结构常数的理论推导。
We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. The dynamics can also predict the values of free parameters of the low energy standard model: these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the exceptional Jordan algebra $J_3(8)$ which describes the three fermion generations. We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra, and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the low energy fine structure constant.
