This is the theory that inspired J.S. Bell's work into the nonlocality of nature. It also is an example of a "hidden variables theory" although the hidden variable here is the position of the particle. The theory is extremely natural if you assume that a particle actually has a definite position. The uncertainty principle, spin, identical particles, and operators as observables all come out of the theory very naturally. Standard QM appears as simply a statistical tool of this deterministic theory. BM has the advantage over QM because it is actually well defined. It also has the advantage of bringing to the forefront the most interesting current conceptual problem: how to reconcile the nonlocality of the quantum world with relativity.

My thesis is organized in the following way: Chapter 2 is an introduction to BM; Chapter 3 discusses the Pauli spin equation and the Dirac equation with a new viewpoint on understanding where these equations come from; Chapter 4 is about how the topology of configuration space influences the formation of Bohmian theories; Chapter 5 applies the results in the case of identical particles; Chapter 6 leaves Bohmian mechanics momentarily to explore derivatives of mappings between manifolds, a topic needed for Chapter 7 (the last half of the chapter is not needed for anything, but addresses the question of Taylor series expansions of mappings between manifolds); Chapter 7 is about two algorithms for finding the solutions of Schrodinger's equation using Bohmian ideas. The appendices have some rather nice material in them. I especially like the final appendix in which I discuss the characteristics of the Hamilton-Jacobi equation and the continuity equation in the general setting of a Riemannian manifold; although the results are not new, I have not seen anyone do it in the way that I did it.

My advisor is Sheldon Goldstein. On his website, you can find his published work on Bohmia n mechanics. They are filled with insight and clarity. My recommendation to start would be Bohmian Mechanics as the Foundation of Quantum Mechanics. For existence and uniqueness of the dynamics, read On the Global Existence of Bohmian Mechanics. To read a wonderful paper that gets at the heart of how the uncertainty principl e is perfectly natural in a deterministic theory, read Quantum Equilibrium and the Origin of Absolute Uncertainty. A paper unrelated to Bohmian mechanics but still very important is Boltzmann's Approach to Statistical Mechanics.