The physical heritage of Sir W.R. Hamilton

Details The physical heritage of Sir W.R. Hamilton The physical heritage of Sir W.R. Hamilton

2002-01-28

arxiv.org/abs/math-ph/0201058v5

Physics

Mathematical Physics

37 pages. Presented at the Conference: "The Mathematical Heritage of Sir William Rowan Hamilton" commemorating the sesquicente

Scientific paper

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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