The Principles of Newtonian and Quantum Mechanics: The Need for Planck's Constant, H

Front Cover
World Scientific, 2001 - Science - 384 pages
0 Reviews
This book deals with the foundations of classical physics from the OC symplecticOCO point of view, and of quantum mechanics from the OC metaplecticOCO point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the OC principle of the symplectic camelOCO, 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 OC metatronOCO 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: From Kepler to SchrAdinger OC and Beyond; Newtonian Mechanics; The Symplectic Group; Action and Phase; Semi-Classical Mechanics; The Metaplectic Group and the Maslov Index; SchrAdinger''s Equation and the Metatron. Readership: Researchers and graduate students in mathematical physics."
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

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
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information