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On Hamilton-Jacobi theory: its geometry and relation to pilot-wave theory

Jeremy Butterfield
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Abstract

This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.

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Jeremy Butterfield. 2003-05-21. On Hamilton-Jacobi theory: its geometry and relation to pilot-wave theory. https://arxiv.org/abs/quant-ph/0210140

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