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arXiv · 1506.00714

Null lifts and projective dynamics

Marco Cariglia
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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.

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Marco Cariglia. 2015-06-02. Null lifts and projective dynamics. https://doi.org/10.1016/j.aop.2015.09.002

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