The principles of Newtonian and quantum mechanics : the need for Planck's constant, h

This work deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", 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 "metatron" 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. This book deals with the foundations of classical physics from the “symplectic” point of view, and of quantum mechanics from the “metaplectic” point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the “principle of the symplectic camel”, 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 “metatron” 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. FOREWORD BY BASIL HILEY; PREFACE; CONTENTS; 1 FROM KEPLER TO SCHRODINGER ... AND BEYOND; 1.1 Classical Mechanics; 1.2 Symplectic Mechanics; 1.3 Action and Hamilton-Jacobi's Theory; 1.4 Quantum Mechanics; 1.5 The Statistical Interpretation of w; 1.6 Quantum Mechanics in Phase Space; 1.7 Feynman's ""Path Integral""; 1.8 Bohmian Mechanics; 1.9 Interpretations; 2 NEWTONIAN MECHANICS; 2.1 Maxwell's Principle and the Lagrange Form; 2.2 Hamilton's Equations; 2.3 Galilean Covariance; 2.4 Constants of the Motion and Integrable Systems; 2.5 Liouville's Equation and Statistical Mechanics Johannes Kepler (b.31571) had to wait for less than hundred years for recognition: in 1687, Sir Isaac Newton (b.1643) published Philosophiae Naturalis Principia Mathematica.