Theoretical Equivalence in Classical Mechanics and its relationship to Duality

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Teh, Nicholas; Tsementzis, Dimitris
preprint description
As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive `equivalence' of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories (via Tulczyjew's Triple) provides a sense in which they are (1) isomorphic, and (2) mutually and canonically definable through an analog of `common definitional extension'.