Analytical Mechanics for Relativity and Quantum Mechanics~tqw~ darksiderg torrent

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Analytical Mechanics for Relativity and Quantum Mechanics
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Type.................: Ebook
Part Size............: 4,108,964 bytes




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Posted by............: ~tqw~

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Release Notes
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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 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 closelyrelated
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.

Table of Contents

1 Basic dynamics of point particles and collections 3
2 Introduction to Lagrangian mechanics 24
3 Lagrangian theory of constraints 46
4 Introduction of Hamiltonian mechanics 71
5 The calculus of variations 88
6 Hamilton\\\'s principle 117
7 Linear operators and dyadics 123
8 Kinematics of rotation 152
9 Rotational dynamics 202
10 Small vibrations about equilibrium 246
11 Lagrangian mechanics with time as a coordinate 267
12 Hamiltonian mechanics with time as a coordinate 285
13 Hamilton\\\'s principle and Noether\\\'s theorem 305
14 Relativity and spacetime 313
15 Fourvectors and operators 343
16 Relativistic mechanics 376
17 Canonical transformations 411
18 Generating functions 434
19 Hamilton-Jacobi theory 461
A Vector fundamentals 495
B Matrices and determinants 508
C Eigenvalue problem with general metric 534
D The calculus of many variables 540
E Geometry of phase space 575

Product Details

* ISBN: 019856726X
* ISBN-13: 9780198567264
* Format: Hardcover, 597pp
* Publisher: Oxford University Press
* Pub. Date: June 2005

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