Analytical Mechanics for Relativity and Quantum Mechanics

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Oliver Johns (Emeritus Professor, Emeritus Professor, Department of Physics, San Francisco State University)

Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns (Emeritus Professor, Emeritus Professor, Department of Physics, San Francisco State University)

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English

Oxford University Press
15 March 2016

Mathematics & Sciences; Classical mechanics; Quantum physics (quantum mechanics & quantum field theory); Relativity physics; Statistical physics

Series: Oxford Graduate Texts

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum mechanics:

Part I is an introduction to analytical mechanics, suitable for a graduate or advanced undergraduate course.

Part II presents material designed principally for graduate students.

The appendices in Part III summarize the mathematical methods used in the text.

The book integrates relativity into the teaching of classical mechanics.

Part II introduces special relativity and covariant mechanics.

It develops extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics, including an extended definition of canonical transformation that both simplifies the theory and no longer excludes the Lorentz transformation.

The book assists students who study classical mechanics as a preparation for quantum mechanics.

Analytical mechanics is presented using methods - such as linear vector operators and dyadics - that familiarize the student with similar operator techniques in quantum theory and the dyadic Dirac notation.

Comparisons to quantum mechanics appear throughout the text.

For example, the chapter on Hamilton-Jacobi theory includes discussions of the closely related Bohm hidden variable model and Feynman path integral method. The chapter on angle-action variables concludes with a section on the old quantum theory. Several of the fundamental problems in physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection. Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics.

New to the Second Edition:

Part I contains new chapters on Central Force Motion (Chapter 11) and Scattering (Chapter 12), and new material on time-independent canonical transformations.

Part II contains a new chapter (Chapter 22) on Angle-Action Variables.

These additions allow a more flexible use of the text.

Part I is now a self-contained, introductory analytical mechanics course.

The instructor can then select a range of topics from Part II appropriate to the interests of more advanced students.

By: Oliver Johns (Emeritus Professor Emeritus Professor Department of Physics San Francisco State University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 244mm, Width: 171mm, Spine: 34mm
Weight: 1g
ISBN: 9780198766803
ISBN 10: 0198766807
Series: Oxford Graduate Texts
Pages: 652
Publication Date: 15 March 2016
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

I: INTRODUCTION: THE TRADITIONAL THEORY 1: Basic Dynamics of Point Particles and Collections 2: Introduction to Lagrangian Mechanics 3: Lagrangian Theory of Constraints 4: Introduction to Hamiltonian Mechanics 5: The Calculus of Variations 6: Hamilton's Principle 7: Linear Operators and Dyadics 8: Kinematics of Rotation 9: Rotational Dynamics 10: Small Vibrations About Equilibrium 11: Two-body Central Force Systems 12: Introduction to Scattering II:MECHANICS WITH TIME AS A COORDINATE 13: Lagrangian Mechanics with Time as a Coordinate 14: Hamiltonian Mechanics with Time as a Coordinate 15: Hamilton's Principle and Noether's Theorem 16: Relativity and Spacetime 17: Fourvectors and Operators 18: Relativistic Mechanics 19: Canonical Transformations 20: Generating Functions 21: Hamilton-Jacobi Theory III: MATHEMATICAL APPENDICES A: Vector Fundamentals B: Matrices and Determinants C: Eigenvalue Problem with General Metric D: The Calculus of Many Variables E: Geometry of Phase Space

Oliver Davis Johns is Professor of Physics Emeritus at San Francisco State University.

Reviews for Analytical Mechanics for Relativity and Quantum Mechanics

Review from previous edition The author deserves to be congratulated on the production of what soon will establish itself as a well-respected and useful book which I am pleased to have on my shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject EL which would not benefit from use of this well-planned and conceived and refreshing presentation. Current Engineering Practice An excellent book on analytical mechanics, which offers both graduate and undergradute students a stimulating read. Contemporary Physics