W.R.爵士的物质遗产汉密尔顿
The physical heritage of Sir W.R. Hamilton
摘要：
在发现四元数150年后，汉密尔顿的猜想，即四元数是物理学的基本语言，被重新评估，并被证明基本上是正确的，只要人们承认经典和量子物理中的复数，并接受相对论形式主义的复杂性。经典动力学、电动力学和量子理论都有例子。Lanczos的，爱因斯坦的，和Petiau的狄拉克方程的推广被证明是非常自然的制定与双四元数。自旋、同位旋和质量量子化的讨论将大大方便。与其他形式相比，双四元数具有给出简洁但同时又显式的公式的优点，这些公式可直接用于代数或数值计算。
英文摘要：
150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and quantum physics, and accepts carrying along the intricacies of the relativistic formalism. Examples are shown in classical dynamics, electrodynamics, and quantum theory. Lanczos's, Einstein's, and Petiau's generalizations of Dirac's equation are shown to be very naturally formulated with biquaternions. The discussion of spin, isospin, and mass quantization is greatly facilitated. Compared with other formalisms, biquaternions have the advantage of giving compact but at the same time explicit formulas which are directly usable for algebraic or numerical calculations.
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