连接电弱发电机和引力发电机
Linking electroweak and gravitational generators
摘要：
利用复杂化的四元数，在SU（2）xU（1）李群的两个不同且令人惊讶的交换四维表示的生成元与自旋（3，1）李群的两个四维自旋1/2表示的生成元之间建立了一个有趣的联系：前者的发生器完全决定了后者的发生器，它们交叉组合构成了两个不同但密切相关的发生器，自旋（3，1）xSU（2）xU（1）的四维表示。这些表示被用来构造一个Spin（3，1）xSU（2）xU（1）规范不变拉格朗日量，它包含两个四旋量，不是通常的由相反螺旋度和相等弱同位旋的Weyl双旋量组成，而是由相反弱同位旋和相等螺旋度的Weyl双旋量组成，这种构造自然地产生于数学形式本身。一个可能的未来推广，使用复杂的八元数，进行了讨论。
英文摘要：
Using complexified quaternions, an intriguing link between generators of two different and surprisingly commuting four-dimensional representations of the SU(2)xU(1) Lie group, and generators of two four-dimensional spin 1/2 representations of the Spin(3,1) Lie group is established: the former generators completely determine the latter ones, and cross-combined they constitute two different, but closely related, four-dimensional representations of Spin(3,1)xSU(2)xU(1). These representations are used to construct a Spin(3,1)xSU(2)xU(1) gauge invariant Lagrangian, containing two four-spinors consisting not as usual of Weyl two-spinors of opposite helicity and equal weak isospin, but instead of Weyl two-spinors of opposite weak isospin and equal helicity, a construction which arises naturally from the mathematical formalism itself. A possible future generalization, using complexified octonions, is discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
