The Principle of Least Action
The Principle of Least Action
£129.00
GBPThe principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.
- Drawing from the original sources, this book discusses many of the key ideas in this area from both the scientific and historical perspectives to paint a broad picture of this unifying principle
- Discusses classic papers in a way that is accessible to the modern reader and will appeal to those who are interested in how physical concepts are generated
- Includes worked examples to show how the principle works in practice
Reviews & endorsements
'I recommend this exciting book to readers interested in how a small number of principles can explain modern physical theory. A major part of this excellent physical, mathematical, and historical study of the principle of least action is the exposition of the optical-mechanical analogy that led to the invention of Schrӧdinger's wave mechanics in 1926 … Containing the mathematical steps of numerous detailed derivations with clearly designed figures to aid the reader, the text is physically and mathematically rigorous and serves as a guide to the next step: the reading of the original papers cited in the references.' Barry R. Masters, Optics & Photonics News
Product details
March 2018Adobe eBook Reader
9781108299862
0 pages
96 b/w illus. 1 table
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. Introduction
- 2. Prehistory of variational principles
- 3. An excursio to Newton's Principia
- 4. The optical-mechanical analogy, part I
- 5. D'Alembert, Lagrange, and the statics-dynamics analogy
- 6. The optical mechanical analogy, part II: the Hamilton–Jacobi equation
- 7. Relativity and least action
- 8. The road to quantum mechanics
- Appendix A. Newton's solid of least resistance using calculus
- Appendix B. Original statement of D'Alembert's principle
- Appendix C. Equations of motion of MacCullagh's ether
- Appendix D. Characteristic function for a parabolic Keplerian orbit
- Appendix E. Saddle paths for reections on a mirror
- Appendix F. Kinetic caustics from quantum motion in one dimension
- Appendix G. Einstein's proof of the covariance of Maxwell's equations
- Appendix H. Relativistic four vector potential
- Appendix I. Ehrenfest's proof of the adiabatic theorem
- References
- Index.
