The physical heritage of Sir W.R. Hamilton
arXiv:math-ph/0201058
Abstract
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.
37 pages. Presented at the Conference: "The Mathematical Heritage of Sir William Rowan Hamilton" commemorating the sesquicentennial of the invention of quaternions. Trinity College, Dublin, 17th -- 20th August, 1993. Revised version with several additional notes and references
References in corpus (3)
Cited by in corpus (9)
- Octonic relativistic quantum mechanics
- Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
- Quaternions in mathematical physics (1): Alphabetical bibliography
- On the physical interpretation of singularities in Lanczos-Newman electrodynamics
- The relations of the homogeneous Maxwell's equations to the theory of functions
- Derivation of the potential, field, and locally-conserved charge-current density of an arbitrarily moving point-charge
- Eigenbundles, Quaternions, and Berry's Phase
- Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra
- A possible fundamental explanation of electroweak unification