Overview

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the graduate level. A distinguishing feature of the book is its integration of special relativity into the teaching of classical mechanics. Extended Lagrangian and Hamiltonian methods are introduced that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Lagrangians and Hamiltonians, canonical transformations, and the Hamilton-Jacobi equation are developed using this extended theory. This permits the Lorentz transformation of special relativity to become a canonical transformation. This is also a book for those who study analytical mechanics as a preliminary to a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text, and classical mechanics itself is presented in a way that will aid the reader in the study of quantum theory. A chapter is devoted to linear vector operators and dyadics, including a comparison to the bra-ket notation of quantum mechanics. Rotations are presented using an operator formalism similar to that used in quantum theory, and the definition of the Euler angles follows the quantum mechanical convention. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. The book provides a necessary bridge to carry graduate students from their previous undergraduate classical mechanics courses to the future study of advanced relativity and quantum theory. Several of the current fundamental problems in theoretical 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. This text is intended to encourage the retention or restoration of introductory graduate analytical mechanics courses. It is written for the intellectually curious graduate student, and the teacher who values mathematical precision in addition to accessibility.

Full Product Details

Author:   Oliver Johns
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 17.50cm , Height: 3.70cm , Length: 24.70cm
Weight:   1.175kg
ISBN:  

9780198567264

ISBN 10:   019856726
Pages:   624
Publication Date:   07 July 2005
Audience:   College/higher education ,  Tertiary & Higher Education
Replaced By:   9780191001628
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

PART I: THE CLASSICAL 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 ; PART II: MECHANICS WITH TIME AS A COORDINATE ; 11. Lagrangian Mechanics with Time as a Coordinate ; 12. Hamiltonian Mechanics with Time as a Coordinate ; 13. Hamilton's Principle and Noether's Theorem ; 14. Relativity and Spacetime ; 15. Fourvectors and Operators ; 16. Relativistic Mechanics ; 17. Canonical Transformations with Time as a Coordinate ; 18. Generating Functions ; 19. Hamilton-Jacobi Theory ; PART III: MATHEMATICAL REFERENCES ; A. Vector Fundamentals ; B. Matrices and Determinants ; C. Eigenvalue Problem with General Metric ; D. The Calculus of Many Variables ; E. Geometry of Phase Space

Reviews

The author deserves to be congratulated on the production of what soon will establish itslef as a well-respected and useful book which I am pleased to have on mu shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject of analytical mechanics for relatively and quantum mechanics which would not benefit from use of this well-planned and conceived and refreshing presentation. Current Engineering Practice. Volume 48 2005

Author Information

For the past 30 years, Professor Johns has taught graduate classical and quantum mechanics courses at San Francisco State University. This teaching experience has given him a sensitivity to the intellectual needs of physics graduate students. For the past fifteen years, he has had an association with the Department of Theoretical Physics at Oxford, making yearly visits. He does research in the foundations of physics: Hidden variable models, foundations of relativity, foundations of quantum mechanics. He has also done research work in theoretical Nuclear Physics and Nuclear Astrophysics, at the Niels Bohr Institute, Orsay, and the CEA laboratories in Paris.

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