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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 introduc

Lagrangian functions. --- Geometric quantization. --- Maslov index.

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514.75 --- Characteristic classes --- Maslov index --- Symplectic geometry --- Geometry, Differential --- Index, Maslov --- Forms, Quadratic --- Lagrangian functions --- Vector spaces --- Classes, Characteristic --- Differential topology --- Differential geometry in spaces with fundamental groups --- 514.75 Differential geometry in spaces with fundamental groups

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Symplectic groups --- Representations of groups --- Forms, Modular --- 514.76 --- Lifting theory --- Maslov index --- Series, Theta --- Groups, Symplectic --- Linear algebraic groups --- Theta series --- Functions, Theta --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Index, Maslov --- Forms, Quadratic --- Lagrangian functions --- Vector spaces --- Measure theory --- Modular forms --- Forms (Mathematics) --- Geometry of differentiable manifolds and of their submanifolds --- 514.76 Geometry of differentiable manifolds and of their submanifolds --- Nombres, Théorie des --- Formes automorphes --- Number theory --- Automorphic forms --- Fonctions thêta --- Opérateurs pseudo-différentiels --- Functions, Theta. --- Number theory. --- Fonctions thêta. --- Nombres, Théories des --- Opérateurs pseudo-différentiels --- Analyse sur une variété