The principles of Newtonian and quantum mechanics : the need for Planck's constant, h / M A de Gosson.

Format:

Book

Author/Creator:

Gosson, Maurice de.

Language:

English

Subjects (All):

Lagrangian functions.

Maslov index.

Geometric quantization.

Physical Description:

1 online resource (382 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., c2001.

Language Note:

English

Summary:

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

Contents:

CONTENTS ; FOREWORD BY BASIL HILEY ; PREFACE ; 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 ; 3 THE SYMPLECTIC GROUP ; 3.1 Symplectic Matrices and Sp(n) ; 3.2 Symplectic Invariance of Hamiitonian Flows ; 3.3 The Properties of Sp(n) ; 3.4 Quadratic Hamiltonians

3.5 The Inhomogeneous Symplectic Group 3.6 An Illuminating Analogy ; 3.7 Gromov's Non-Squeezing Theorem ; 3.8 Symplectic Capacity and Periodic Orbits ; 3.9 Capacity and Periodic Orbits ; 3.10 Cell Quantization of Phase Space ; 4 ACTION AND PHASE ; 4.1 Introduction

4.2 The Fundamental Property of the Poincare-Cartan Form 4.3 Free Symplectomorphisms and Generating Functions ; 4.4 Generating Functions and Action ; 4.5 Short-Time Approximations to the Action ; 4.6 Lagrangian Manifolds ; 4.7 The Phase of a Lagrangian Manifold

4.8 Keller-Maslov Quantization

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [343]-351) and index.

ISBN:

9786611865986

9781281865984

1281865982

9781848161429

1848161425

OCLC:

815741824