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

• Autore: Gosson Maurice de
• Pubblicazione: London, : Imperial College Press; River Edge, NJ, : Distributed by World Scientific Pub., c2001
• Descrizione fisica: 1 online resource (382 p.)
• Disciplina: 530.12
• Soggetto topico: Lagrangian functions; Maslov index; Geometric quantization
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [343]-351) and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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
• Titolo autorizzato: The principles of Newtonian and quantum mechanics
• ISBN: 1-281-86598-2; 9786611865986; 1-84816-142-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910454264803321
• Lo trovi qui: Univ. Federico II