Summary: The canonical map τ of the field of quaternions ℍ to SO(E) yields a logarithmic scale on the centre ℝ·e of ℍ; here E=e ⊥ with e being the unit element of ℍ. Together with a harmonic oscillator, the logarithmic scale and Runge-Lenz vector, the map τ corresponds to a Kepler motion on a conic section in symplectic plane P. The action of dilations of metaplectic group on the propagators on the light cone of the wave equation and logarithmic scale on the centre of the Heisenberg group G=ℝ·e+P yield Kepler's third law. This is related to Bradley's aberration method to verify optically the motion of the Earth around the Sun.
Dieser Eintrag ist Teil der Universitätsbibliographie.
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