arXiv:math-ph/0604063math-ph
Geometric Hamilton-Jacobi Theory
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Abstract
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints. We also consider the example of the free relativistic particle, the rigid body and the electron-monopole system.
I didn't read the paper yet and it really might contain some valuable insights into the nature of quantum mechanics (I'll take a look at it later today), but I find this debate about whether the wave-function is a real object or not hilarious: It completely fails to take into…
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