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*******************************************************************************<br /> Analytical Mechanics for Relativity and Quantum Mechanics<br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 4,108,964 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> This book provides an innovative and mathematically sound treatment of the <br /> foundations of analytical mechanics and the relation of classical mechanics to <br /> relativity and quantum theory. It is intended for use at the graduate level. A <br /> distinguishing feature of the book is its integration of special relativity into <br /> the teaching of classical mechanics. Extended Lagrangian and Hamiltonian methods <br /> are introduced that treat time as a transformable coordinate rather than the <br /> fixed parameter of Newtonian physics. Advanced topics such as covariant <br /> Lagrangians and Hamiltonians, canonical transformations, and the Hamilton-Jacobi <br /> equation are developed using this extended theory. This permits the Lorentz <br /> transformation of special relativity to become a canonical transformation.<br /> <br /> This is also a book for those who study analytical mechanics as a preliminary to <br /> a critical exploration of quantum mechanics. Comparisons to quantum mechanics <br /> appear throughout the text, and classical mechanics itself is presented in a way <br /> that will aid the reader in the study of quantum theory. A chapter is devoted to <br /> linear vector operators and dyadics, including a comparison to the bra-ket <br /> notation of quantum mechanics. Rotations are presented using an operator <br /> formalism similar to that used in quantum theory, and the definition of the <br /> Euler angles follows the quantum mechanical convention. The extended Hamiltonian <br /> theory with time as a coordinate is compared to Dirac\\\'s formalism of primary <br /> phase space constraints. The chapter on relativistic mechanics shows how to use <br /> covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The <br /> chapter on Hamilton-Jacobi theory includes a discussion of the closelyrelated <br /> Bohm hidden variable model of quantum mechanics. The book provides a necessary <br /> bridge to carry graduate students from their previous undergraduate classical <br /> mechanics courses to the future study of advanced relativity and quantum theory. <br /> Several of the current fundamental problems in theoretical physics---the <br /> development of quantum information technology, and the problem of quantizing the <br /> gravitational field, to name two---require a rethinking of the quantum-classical <br /> connection. This text is intended to encourage the retention or restoration of <br /> introductory graduate analytical mechanics courses. It is written for the <br /> intellectually curious graduate student, and the teacher who values mathematical <br /> precision in addition to accessibility. <br /> <br /> Table of Contents<br /> <br /> 1 Basic dynamics of point particles and collections 3<br /> 2 Introduction to Lagrangian mechanics 24<br /> 3 Lagrangian theory of constraints 46<br /> 4 Introduction of Hamiltonian mechanics 71<br /> 5 The calculus of variations 88<br /> 6 Hamilton\\\'s principle 117<br /> 7 Linear operators and dyadics 123<br /> 8 Kinematics of rotation 152<br /> 9 Rotational dynamics 202<br /> 10 Small vibrations about equilibrium 246<br /> 11 Lagrangian mechanics with time as a coordinate 267<br /> 12 Hamiltonian mechanics with time as a coordinate 285<br /> 13 Hamilton\\\'s principle and Noether\\\'s theorem 305<br /> 14 Relativity and spacetime 313<br /> 15 Fourvectors and operators 343<br /> 16 Relativistic mechanics 376<br /> 17 Canonical transformations 411<br /> 18 Generating functions 434<br /> 19 Hamilton-Jacobi theory 461<br /> A Vector fundamentals 495<br /> B Matrices and determinants 508<br /> C Eigenvalue problem with general metric 534<br /> D The calculus of many variables 540<br /> E Geometry of phase space 575<br /> <br /> Product Details<br /> <br /> * ISBN: 019856726X<br /> * ISBN-13: 9780198567264<br /> * Format: Hardcover, 597pp<br /> * Publisher: Oxford University Press<br /> * Pub. Date: June 2005<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> Adobe Acrobat Reader<br />