Analytical Mechanics for Relativity and Quantum Mechanics 1st Edition by Oliver Johns 9781435609259 1435609255

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Product details:

ISBN 10: 1435609255

ISBN 13: 9781435609259

Author: Oliver Johns

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. 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, 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 familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics, such as the development of quantum information technology and the problem of quantising the gravitational field, require a rethinking of the quantum-classical connection.

Table of contents:

Part I Introduction: The Traditional Theory

1 Basic Dynamics of Point Particles and Collections

2 Introduction to Lagrangian Mechanics

3 Lagrangian Theory of Constraints

4 Introduction To Hamiltonian Mechanics

5 The Calculus of Variations

6 Hamilton’s Principle

7 Linear Operators and Dyadics

8 Kinematics of Rotation

9 Rotational Dynamics

10 Small Vibrations About Equilibrium

Part II Mechanics with Time as a Coordinate

11 Lagrangian Mechanics with Time as a Coordinate

12 Hamiltonian Mechanics with Time as a Coordinate

13 Hamilton’s Principle and Noether’s Theorem

14 Relativity and Spacetime

15 Fourvectors and Operators

16 Relativistic Mechanics

17 Canonical Transformations

18 Generating Functions

19 Hamilton–Jacobi Theory

Part III MATHEMATICAL APPENDICES

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Tags: Oliver Johns, Analytical, Mechanics, Relativity