Maurice A de Gosson, Basil Hiley
WSPC; 2nd edition
The “The Principles of Newtonian and Quantum Mechanics: The Need for Planck’s Constant; h” 2nd edition of this PDF ebook deals; as the first; with the foundations of classical physics from the “symplectic” point of view; and of quantum mechanics from the “metaplectic” point of view. We have revised and augmented the topics studied in the 1st edition in the light of new results; and added many new sections. The Bohmian interpretation of quantum mechanics is discussed in good detail. Phase space quantization is achieved using the “principle of the symplectic camel”; which is a deep topological property of Hamiltonian flows. We introduce the notion of “quantum blob”; which can be viewed as the fundamental phase space unit. The mathematical tools developed in this ebook are 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. The concept of the “metatron” is introduced; in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.