On Hamilton-Jacobi theory: its geometry and relation to pilot-wave theory
Quantum Physics
2007-05-23 v2 Classical Physics
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.
Cite
@article{arxiv.quant-ph/0210140,
title = {On Hamilton-Jacobi theory: its geometry and relation to pilot-wave theory},
author = {Jeremy Butterfield},
journal= {arXiv preprint arXiv:quant-ph/0210140},
year = {2007}
}
Comments
31 pages, no figures. Minor corrections and changes made since previous version. This version is forthcoming in Elitzur, A.C., Dolev, S., and Kolenda, N. (editors), `Quo Vadis Quantum Mechanics? Possible Developments in Quantum Theory in the 21st Century', New York: Springer, 2004