Maurice A de Gosson, Basil Hiley
WSPC; 2nd edition
This PDF ebook's second edition, titled “The Principles of Newtonian and Quantum Mechanics: The Need for Planck's Constant,” deals, as did the first edition, with the foundations of classical physics from the “symplectic” point of view and the foundations of quantum mechanics from the “metaplectic” point of view, respectively. In light of new findings, the themes that were covered in the first edition have been updated, expanded, and edited, and numerous new parts have been added. In this article, the Bohmian interpretation of quantum physics is examined in some depth. The “principle of the symplectic camel,” which is a fundamental topological property of Hamiltonian flows, is utilized in order to accomplish the goal of phase space quantization. We present the idea of a “quantum blob,” which is a fundamental phase space unit and can be thought of as such. The theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes are the three mathematical tools that are developed throughout the course of the reading of this ebook. Within the context of the Bohmian theory of motion, the notion of the “metatron” is presented. The behavior of the propagator over short periods of time is investigated and then used to the quantum Zeno effect.