论文标题
克利福德代数的亚组
Subgroups of Clifford algebras
论文作者
论文摘要
克利福德代数用于构建自旋组，因此在量子力学理论中特别重要。但是自旋组并不是克利福德代数的唯一子群。代数主义者对这些群体和代数的观点可能会提出可以更广泛地应用它们来描述物质的基本特性的方法。我没有声称在基本代数之上建立物理理论，我对可能的物理解释的建议仅是指示性的，并且可能行不通。然而，三代费米子的存在和弱相互作用的对称性破坏似乎自然而然地源于dirac代数从复数到四元素的延伸。
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on these groups and algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations of fermions and the symmetry-breaking of the weak interaction seem to emerge naturally from an extension of the Dirac algebra from complex numbers to quaternions.
