I propose using the group $\text{SL}(4,ℝ)$ as a generalization of the Dirac group $\text{SL}(2,ℂ)$ used in quantum mechanics, in an attempt to match the symmetries of the ‘internal’ spacetime of elementary particles to the symmetries of the ‘external’ spacetime of general relativity. While my conclusions do not amount to a new model or theory, they do highlight some specific points where there are apparent conflicts between the mathematics and the physics of the standard model, that might repay closer investigation. As evidence that this mathematical approach may have interesting things to say about physics, I propose two mass equations that seem not to have been observed previously.

我建议使用该组$\text{SL}(4,ℝ)$作为狄拉克群的推广$\text{SL}(2,ℂ)$用于量子力学，试图将基本粒子的“内部”时空的对称性与广义相对论的“外部”时空的对称性相匹配。虽然我的结论并不构成一个新的模型或理论，但它们确实突出了标准模型的数学和物理之间存在明显冲突的一些具体点，这可能会得到更深入的研究。为了证明这种数学方法可能对物理学有有趣的看法，我提出了两个以前似乎没有观察到的质量方程。