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arXiv · 1503.07802

The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics

Marco Cariglia·Filipe Kelmer Alves
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Abstract

This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics in an enlarged space. We point out that it can be easily obtained from basic principles of Hamiltonian dynamics, and as such it represents a useful didactical way to introduce graduate students to several modern concepts of geometry applied to physics: curved spaces, both Riemannian and Lorentzian, conformal transformations, geometrisation of interactions and extra dimensions, geometrisation of dynamical symmetries. For all these concepts the Eisenhart lift can be used as a theoretical tool that provides easily achievable examples, with the added benefit of also being a topic of current research with several applications, among which the study of dynamical systems and non-relativistic holography.

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Marco Cariglia, Filipe Kelmer Alves. 2015-03-02. The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics. https://doi.org/10.1088/0143-0807%2F36%2F2%2F025018

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