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Analytical Mechanics for Relativity and Quantum Mechanics
Analytical Mechanics for Relativity and Quantum Mechanics is 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.
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.
- GenresPhysics
624 pages, Hardcover
First published September 1, 2005
28 people want to read
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Displaying 1 of 1 review
October 8, 2023
Amazone
Best there is?
My classmates & I hated this book when we took graduate mechanics. But three years later after struggling through Sakurai and Peskin & Schroeder I must admit this book gave me a solid grasp of Lagrangians and Hamiltonians.
I would have often been lost without having studied this text first.In fact, Dr. Johns purposely designed this text on mechanics as a bridge to graduate quantum mechanics.
[After all, what other point is there to studying this subject at this level? The approach fails when things like friction come into play and if you want practical mechanics your time is better spent doing the computer problems in books like Fowler & Cassidy which are more realistic.]
Compared to Goldstein or Landau & Lifschitz it's a model of clarity and providing an appropriate level of support for first year grad students.
The subject matter is hard, the problems are hard. They have to be if you want to learn physics at the graduate level. Five stars since there is nothing better for this level.
My only real complaint with the book is that the vast majority of my time solving the problems was spent doing very complicated algebra.
Ten minutes of physics, hours of manipulating equations with page after page of algebra.
Is it truly not possible to make difficult grad problems without spending most of your time on algebra? It makes impossible to use the answers in the back of the book because they take too long to see to completion.
moratati
Best there is?
My classmates & I hated this book when we took graduate mechanics. But three years later after struggling through Sakurai and Peskin & Schroeder I must admit this book gave me a solid grasp of Lagrangians and Hamiltonians.
I would have often been lost without having studied this text first.In fact, Dr. Johns purposely designed this text on mechanics as a bridge to graduate quantum mechanics.
[After all, what other point is there to studying this subject at this level? The approach fails when things like friction come into play and if you want practical mechanics your time is better spent doing the computer problems in books like Fowler & Cassidy which are more realistic.]
Compared to Goldstein or Landau & Lifschitz it's a model of clarity and providing an appropriate level of support for first year grad students.
The subject matter is hard, the problems are hard. They have to be if you want to learn physics at the graduate level. Five stars since there is nothing better for this level.
My only real complaint with the book is that the vast majority of my time solving the problems was spent doing very complicated algebra.
Ten minutes of physics, hours of manipulating equations with page after page of algebra.
Is it truly not possible to make difficult grad problems without spending most of your time on algebra? It makes impossible to use the answers in the back of the book because they take too long to see to completion.
moratati
Displaying 1 of 1 review