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Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics
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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 treats time as a transformable coordinate, and so moves the teaching of classical mechanics out of the ninteenth century and into the modern relativistic era. It also presents of classical mechanics in a way designed to assist the student's transition to quantum theory. - ;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 introductory graduate level. A distinguishing feature of the book is its integration of special relativity 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 as covariant 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 space constraints. The chapter on relativisitic 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, that will familiarize the

student with similar techniques in 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. 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. - ;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 -