Classical and Quantic Periodic Motions of Multiply Polarized Spin-Particles
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:The author of this volume defines a diffusion flow for a variational problem lacking completeness related to the geometry of a contact form a a and a vector field u in its kernel. He analyzes the ends of the flow lines and finds them to be of two types: one involving periodic orbits of the Reeb (Hamiltonian) vector field x, and the other where asymptotes occur. In the most general case these turn out to be periodic motions for x up to quantic jumps of a very special type along u. He shows that the mathematical results and the physical interpretation fit and provide new points of view useful in the foundations of quantum mechanics.
Table of Contents
Technical Construction of a Diffusion Flow and Convergence Theorems
The Variational Problem at Infinity
The Underlying Variational Space
The Classical Periodic Motions
Appendix 1: Some Technical Justifications
Appendix 2: The Dynamics of a (see symbol) along v (see symbol): Basic Computations
Appendix 3: Some Additional Remarks About the Physical Interpretation, Two Mathematical Conjectures
Appendix 4: How to Take Care of the Problem of the Small Normals