Null lifts and projective dynamics
arXiv:1506.00714 · doi:10.1016/j.aop.2015.09.002
Abstract
We describe natural Hamiltonian systems using projective geometry. The null lift procedure endows the tangent bundle with a projective structure where the null Hamiltonian is identified with a projective conic and induces a Weyl geometry. Projective transformations generate a set of known and new dualities between Hamiltonian systems, as for example the phenomenon of coupling-constant metamorphosis. We conclude outlining how this construction can be extended to the quantum case for Eisenhart-Duval lifts.
11 pages, no figures. Some minor changes, typos amended
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- Finslerian geometrization of quantum mechanics in the hydrodynamical representation
- "Kepler Harmonies" and conformal symmetries
- A Hamiltonian approach to the gradient-flow equations in information geometry
- How the modified Bertrand theorem explains regularities of the periodic table I. From conformal invariance to Hopf mapping
- Conformal Triality of the Kepler problem
- Spectral intertwining relations in exactly solvable quantum-mechanical systems
- Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2