关于用双四元数或Clifford数表述和推广Dirac方程、Proca方程和Maxwell方程的评论
Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers
摘要：
当代研究者试图用双四元数或克利福德数来改写或推广狄拉克、普罗卡或麦克斯韦的理论时遇到的许多解释困难，在很久以前就已经被包括兰佐斯、普罗卡和爱因斯坦在内的许多物理学家遇到了。在古尔西开创的现代方法中，这些困难通过认识到大多数推广导致描述不同内禀自旋和同位旋的粒子的叠加的理论而得到解决，因此正确的解释出现在完全庞加莱协方差的要求中，包括空间和时间反转，以及反转和规范不变性。例如，狄拉克方程最简单的推广所隐含的解的数量的加倍（即，Lanczos方程）可以解释为同位旋。在这种方法中，双四元数和克利福德数成为以非常优雅和紧凑的方式制定基本粒子标准模型及其许多可能的推广的强大机会。
英文摘要：
Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists including Lanczos, Proca, and Einstein. In the modern approach initiated by Gursey, these difficulties are solved by recognizing that most generalizations lead to theories describing superpositions of particles of different intrinsic spin and isospin, so that the correct interpretation emerges from the requirement of full Poincare covariance, including space and time reversal, as well as of reversion and gauge invariance. For instance, the doubling of the number of solutions implied by the simplest generalization of Dirac's equation (i.e., Lanczos's equation) can be interpreted as isospin. In this approach, biquaternions and Clifford numbers become powerful opportunities to formulate the Standard Model of elementary particles, as well as many of its possible generalizations, in very elegant and compact ways.
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