The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem

Details The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem

Aug 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36..349v&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, Aug. 1985, p. 349-364. CNR-supported research.

Mathematics

12

Kepler Laws, Manifolds (Mathematics), Orbital Mechanics, Transformations (Mathematics), Coordinate Transformations, Equations Of Motion, Quaternions

Scientific paper

In a previous note the author has shown that the KS-transformation may be formulated in terms of hypercomplex numbers. In the present note it is shown, first, that this formulation allows a straight derivation of the Hopf fibering of the sphere S3 (characterized by unit quaternions) having the base space given by the sphere S2 (characterized by unit vectors), and secondly that the KS-transformation allows the "quantization of the symplectic manifold S2" in the sense of Souriau, the associated quantum manifold S3 having a contact structure given by the bilinear relation characteristic of the KS-theory. Furthermore, after presenting a natural extension of the hypercomplex KS-transformation to the full phase space of the Kepler problem, it is shown that this extension allows the quantization of the manifold of Kepler orbits of fixed negative energy.

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