Principles Of Newtonian And Quantum Mechanics, The - The Need For Planck's Constant, H

This book deals with the foundations of classical physics from the "e;symplectic"e; point of view, and of quantum mechanics from the "e;metaplectic"e; point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "e;principle of the symplectic camel"e;, which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "e;metatron"e; is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation.