论文标题
$ su（3）$的最新结果和几何代数方法中的八元成果
Some recent results for $SU(3)$ and Octonions within the Geometric Algebra approach to the fundamental forces of nature
论文作者
论文摘要
探索了几何代数方法中代表$ su（3）$的不同方式。作为其中的一部分，我们考虑了$ su（3）$的特征多生物，以及它们如何与发电机分解为通勤双分类器相关。这项工作的设置在6D欧几里得Clifford代数范围内。然后，我们继续考虑粒子物理学的基本力是否可能来自时空的4D几何代数 - STA。作为其中的一部分，在Sta中完全发现了$ su（3）$的代表，涉及保存双向主义规范。我们还展示了如何在时空代数中充分代表八元，我们认为这对于使它们在物理和工程领域的新社区来说是可以理解和访问的。纸张的两条线被绘制在一起，以显示保留八元标准的方式与保留粒子狄拉克电流的时光部分相同。这暗示了一种在粒子物理学中保存的对称性的新模型。紧随Günaydin和Gürsey在Quarks和Octonions之间的联系以及Octonionion乘法链中的链接之后，我们展示了这两者在我们的方案中如何很好地符合我们的计划，并提供了涉及的操作的一些完全符合的STA版本，在这些情况下，在这些情况下，这些案例可以轻松地理解4Dester的等值。还考虑了与包含$ SU（3）$的较大组的链接，例如$ G_2 $和$ SU（8）$。
Different ways of representing the group $SU(3)$ within a Geometric Algebra approach are explored. As part of this we consider characteristic multivectors for $SU(3)$, and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime -- the STA. As part of this, a representation of $SU(3)$ is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme, and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing $SU(3)$, such as $G_2$ and $SU(8)$, are also considered.
