Analytical Mechanics for Relativity and Quantum Mechanics
Series: Oxford Graduate Texts;
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Product details:
- Edition number 2
- Publisher OUP Oxford
- Date of Publication 19 May 2011
- ISBN 9780191001628
- Binding Hardback
- No. of pages652 pages
- Size 244x178x37 mm
- Weight 1446 g
- Language English
- Illustrations 89 b/w line drawings 0
Categories
Short description:
An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It presents classical mechanics in a way designed to assist the student's transition to quantum theory.
MoreLong description:
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 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, 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.
I think that this is an excellent book on analytical mechanics, which offers both graduate and undergradute students a stimulating read.
Table of Contents:
I: INTRODUCTION: THE TRADITIONAL THEORY
Basic Dynamics of Point Particles and Collections
Introduction to Lagrangian Mechanics
Lagrangian Theory of Constraints
Introduction to Hamiltonian Mechanics
The Calculus of Variations
Hamilton's Principle
Linear Operators and Dyadics
Kinematics of Rotation
Rotational Dynamics
Small Vibrations About Equilibrium
Two-body Central Force Systems
Introduction to Scattering
II:MECHANICS WITH TIME AS A COORDINATE
Lagrangian Mechanics with Time as a Coordinate
Hamiltonian Mechanics with Time as a Coordinate
Hamilton's Principle and Noether's Theorem
Relativity and Spacetime
Fourvectors and Operators
Relativistic Mechanics
Canonical Transformations
Generating Functions
Hamilton-Jacobi Theory
III: MATHEMATICAL APPENDICES
Vector Fundamentals
Matrices and Determinants
Eigenvalue Problem with General Metric
The Calculus of Many Variables
Geometry of Phase Space
