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

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World Scientific, Oct 15, 2001 - Science - 384 pages
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.
 

Contents

1 FROM KEPLER TO SCHRODINGER AND BEYOND
1
2 NEWTONIAN MECHANICS
37
3 THE SYMPLECTIC GROUP
77
4 ACTION AND PHASE
127
5 SEMICLASSICAL MECHANICS
179
6 THE METAPLECTIC GROUP AND THE MASLOV INDEX
221
7 SCHRODINGERS EQUATION AND THE METATRON
267
A Symplectic Linear Algebra
323
B The LieTrotter Formula for Flows
327
C The Heisenberg Groups
331
D The Bundle of SDensities
335
E The Lagrangian Grassmannian
339
BIBLIOGRAPHY
343
INDEX
353
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