Analytical Mechanics for Relativity and Quantum Mechanics

Hardcover | June 19, 2011

byOliver Johns

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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 introductory graduate level. A distinguishing feature of the book is its integration of specialrelativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such ascovariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase spaceconstraints. 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. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, which will familiarize the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics - the development of quantum informationtechnology, 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 undergraduatetraining and advanced study in analytical mechanics, relativity, and quantum mechanics.

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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 introductory graduate level. A distinguishing feature of the book is its integration of specialrelativity into teaching of classical mechanic...

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 Ph...

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Format:HardcoverDimensions:656 pages, 9.69 × 6.73 × 1.47 inPublished:June 19, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0191001627

ISBN - 13:9780191001628

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Table of Contents

I: Introduction: The Traditional Theory1. Basic Dynamics of Point Particles and Collections2. Introduction to Lagrangian Mechanics3. Lagrangian Theory of Constraints4. Introduction to Hamiltonian Mechanics5. The Calculus of Variations6. Hamilton's Principle7. Linear Operators and Dyadics8. Kinematics of Rotation9. Rotational Dynamics10. Small Vibrations About Equilibrium11. Two-body Central Force Systems12. Introduction to ScatteringII: Mechanics with Time as a Coordinate13. Lagrangian Mechanics with Time as a Coordinate14. Hamiltonian Mechanics with Time as a Coordinate15. Hamilton's Principle and Noether's Theorem16. Relativity and Spacetime17. Fourvectors and Operators18. Relativistic Mechanics19. Canonical Transformations20. Generating Functions21. Hamilton-Jacobi TheoryIII: Mathematical AppendicesA. Vector FundamentalsB. Matrices and DeterminantsC. Eigenvalue Problem with General MetricD. The Calculus of Many VariablesE. Geometry of Phase Space

Editorial Reviews

"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 onthe 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