Second Edition Overview

The second edition of this book 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 first edition in the light of new results, and added several new sections.

Topics Covered

The Bohmian interpretation of quantum mechanics is discussed in 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.

Mathematical Tools

The mathematical tools developed in this book 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.

Additional Topics

The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.